This was one of the hottest topics in medieval Jewish philosophy.
Saadia Gaon devoted the first treatise of Emunot V'Deiot to proving creatio ex nihilo and refuting the opposing arguments.
Here is an excerpt from his introduction to that treatise:
Therefore, O thou that seekest the truth, may God be gracious unto thee, if our discussion yield to thee any conclusion of such a nature as [for example] the doctrine of creatio ex nihilo, do not hasten to reject it, since it was precisely something like this that thou didst look for from the beginning of thy quest, and [since] whoever else goes out in search of the truth does likewise. Hear, rather, and realize that thy proofs are stronger than those of the others and that thou art in possession of arguments by means of which thou canst refute any faction of them. Furthermore thou hast over them the advantage of being in possession of miracles and marvels that have been established for thee [as trustworthy]. Therefore hold on to the following three points in every chapter of this book: namely, (a) that thy proofs are stronger than those of the others, (b) that thou art able to refute anyone that disagrees with thee, and (c) that the miracles of thy prophets are a part of thy advantage. (Rosenblatt translation)
R. Bahya Ibn Paquda addressed creation in his Chovot Halevavot in Chapter Five of "The Gate of Unity". He claims to have proved creatio ex nihilo on the basis of three premises:
- Something cannot create itself.
- There must be a first cause which is preceded by no prior cause.
- Anything composite must have been generated.
Rambam devoted a sizable chunk of Book II of Guide for the Perplexed to the question of creation vs eternity. He essentially argued that nothing could be proven, but the arguments in favor of creatio ex nihilo are more plausible, and we accept it based on tradition. In Chapter 25 he explains how the Aristotelian view of an eternal universe is incompatible with Judaism, but the Platonic view of eternal matter can be compatible with Judaism, but both are rejected in any case due to lack of proof:
If we were to accept the Eternity of the Universe as taught by Aristotle, that everything in the Universe is the result of fixed laws, that Nature does not change, and that there is nothing supernatural, we should necessarily be in opposition to the foundation of our religion, we should disbelieve all miracles and signs, and certainly reject all hopes and fears derived from Scripture, unless the miracles are also explained figuratively. The Allegorists amongst the Mohammedans have done this, and have thereby arrived at absurd conclusions. If, however, we accepted the Eternity of the Universe in accordance with the second of the theories which we have expounded above (ch. xxiii.), and assumed, with Plato, that the heavens are likewise transient, we should not be in opposition to the fundamental principles of our religion; this theory would not imply the rejection of miracles, but, on the contrary, would admit them as possible. The Scriptural text might have been explained accordingly, and many expressions might have been found in the Bible and in other writings that would confirm and support this theory. But there is no necessity for this expedient, so long as the theory has not been proved. As there is no proof sufficient to convince us, this theory need not be taken into consideration, nor the other one; we take the text of the Bible literally, and say that it teaches us a truth which we cannot prove; and the miracles are evidence for the correctness of our view. (Friedlander translation)
R. Yehuda Halevi, like Rambam asserts that philosophy can only take us so far in this question, and we ultimately submit to the superiority of our tradition. Like Rambam as well, he does not feel that creation from eternal matter would be in fundamental opposition to the religion.
Ralbag may have devoted the most attention to this issue. The entire Book VI of his Milchamot Hashem is devoted to the question of creation. While he agreed with Rambam and R. Yehuda Helevi that creation from eternal matter is not fundamentally opposed to Judaism, he went much further. He himself believed and promoted this view, and claimed to have proven it; not only that, he argued that this was the view taught by the Torah, and that creatio ex nihilo and an eternal universe are both philosophically untenable. In the last chapter of part one of Book VI, he notes that all of his predecessors were wrong about this question:
Finally, concerning creation of the universe we did not find in any of our predecessors a true philosophical account, other than what is found in the Torah by way of tradition. What we have found in Maimonides almost closes the door against this inquiry. For he advances a theory of creation that is clearly impossible [i.e. creation ex nihilo], and in addition declares that it is impossible for man to reach the truth on this topic by philosophical means. It is therefore quite marvelous that we have actually succeeded in solving these extremely profound problems and in eliminating all the doubts pertaining to them. It is proper, therefore, to give thanks to the Lord (may he be blessed) Who has revealed to us these marvelous and profound truths. May He be eternally blessed and exalted beyond all praise and blessing. (Feldman translation)
The differences between Ralbag's view and Rambam's and R. Judah Halevi's view is aptly summed up by Seymour Feldman in his introduction to his translation of Book VI of Milchamot Hashem:
Indeed, whereas Yehudah Halevi confined himself to a cautious, conciliatory judgement that either hypothesis was acceptable from a religious point of view, and Maimonides suggested that although creation ex nihilo was the preferred doctrine from the point of view of tradition, the Platonic theory would be compatible with Scripture, Gersonides claims that the creation ex nihilo doctrine is absolutely false, indeed absurd.
As mentioned in my answer here Ralbag's view of creation was one of the things that made him a "radical" Jewish thinker. Indeed, he was heavily criticized by later Jewish thinkers.
Ralbag does, though, explicitly address your issue that the existence of eternal matter is akin to having multiple deities. In Chapter 18 of Part 1 of Book VI he writes:
Third difficulty. It might be thought that if there were another eternal thing besides God, it would be a deity like Him. But this is an absolutely shameful [idea]. (Feldman translation)
Reply to third objection. This objection is weak. It does not follow when we posit this body to be eternal that it is on the same level of being as God, so that it is divine like Him. For God is not divine because He is eternal and all other things are not. For even if it were possible that everything were eternal, God alone would be the deity, since He governs everything and gives them their law and order which they possess. In short, God is the deity precisely because of His great level [of perfection], from whose great wisdom and power emanate the beneficial order and rightness found in existent things. The eternal body, however, has no such features, but is utterly and essentially deprived of goodness. And it is the case that whatever attains a greater degree of goodness is therefore more noble; so that man is more noble than an animal and an animal is more noble than a plant. Accordingly, it is clear that this body is utterly defective, whereas God is absolutely perfect. Consequently, this body has no share in divinity at all; for it is farther away from divinity than anything else. And so this rhetorical objection has been removed. (Feldman translation)
R. Hasdai Crescas devoted five chapters to creation in Ohr Hashem 3:1:1. He briefly summarized Aristotle's, Rambam's, and Ralbag's arguments, and then laid out his own view that creatio ex nihilo is a fundamental tenet of Judaism. As he says in the beginning of Chapter 5:
ושהכפירה בו הריסה בשרשי התורה ואולם איננו יסוד ופינה שלא יצויר מציאות התורה זולתו
And that denial of it is a destruction of the foundations of the Torah. However, it is not a foundation and a cornerstone without which the existence of the Torah cannot be conceived.
R. Yosef Albo similarly argues in Chapter 12 of Part 1 of Sefer HaIkkarim that creatio ex nihilo is an obligatory belief, but he does not think it is fundamentally opposed to the Torah, and that is why Rambam did not count it in his listing of the Thirteen Principles.
From then on, creatio ex nihilo has been the basically entirely dominant Jewish view. For several hundred years, Jewish philosophy mostly fell by the wayside, and much of the thought of the "rationalist rishonim" was largely ignored. Thus, today, this is the belief that is, to the best of my knowledge, taught in all (Orthodox) Jewish schools, and if you tell an average Jew that you believe in creation from eternal matter, or the eternity of the universe, you will likely be deemed a heretic.
However, with the advent of modern academic Jewish studies, there is a cadre of people who have been rejuvenating the rationalist rishonim, and bringing some of their ideas back into the public Jewish arena. So, perhaps the tide will yet swing, and some of the other views of creation might gain more popularity (but probably not so likely).
We would be remiss if we did not also mention the minority view of some scholars, that Rambam's advocacy of creatio ex nihilo is merely the exoteric reading of Guide for the Perplexed, while the true esoteric meaning is that Rambam actually agreed with the Aristotelian view of the eternity of the universe. As briefly summarized by Seymour Feldman in his introduction to his translation of Book VI of Milchamot Hashem:
Ever since the Middle Ages there has been an "esoteric" reading of The Guide according to which Maimonides' real doctrine is not creation ex nihilo — the "exoteric teaching" — but some form of the eternity theory. This was the interpretation of his medieval commentators Joseph ibn Kaspi and Moses Narboni; indeed, it was the interpretation of his translator Samuel ibn Tibbon. In recent years this reading of The Guide has been advocated by Leo Strauss and Shlomo Pines, the most recent translator of the Guide into English.
So, to briefly summarize: the majority position within Jewish tradition has apparently always been creatio ex nihilo. Rambam and R. Yehuda Halevi indicated that they would theoretically be okay with creation from eternal matter, while Ralbag went further and uniquely argued that creation from eternal matter is the only possibility. A small group perhaps even held some form of an eternal universe. The ex nihilo team largely seems to have won, and for the most part it is currently a dead issue. You are unlikely to find much current serious discussion of the various positions. Most people have simply accepted ex nihilo and moved on.