Would the Rambam be fine with String Theory being that String Theory involves what happened before the world was created (the big bang) and beyond our universe?
I believe you are referring to Chagigah 16a:
The mishna taught: Whoever looks at four things, it would have been better for him had he never entered the world: Anyone who reflects upon that which is above the firmament; that which is below the earth; what was before the creation of the world; and what will be after the end of the world. The Gemara asks: Granted, it is prohibited to reflect on what is above, what is below, and what is after. This is fine, since one is examining things that are not part of the world but lie beyond it. But before the creation of the world, what has happened has happened. Why is it prohibited to reflect upon this?
The Gemara explains: Rabbi Yoḥanan and Rabbi Elazar both say: This can be demonstrated through a parable with regard to a flesh-and-blood king who said to his servants: Build for me large palaces on a garbage dump. They went and built them for him. Clearly, in that case, the king does not desire that they mention the garbage dump. Here too, God does not want people to concern themselves with the chaos that preceded the world. (Translation and elaboration from Sefaria.org)
Here we see that it is not proper to ponder certain questions.
Yet, Rambam clearly holds (Mishne Torah, Foundation of Faith 2:2) that there is an obligation to study the wisdom of Creation as a path to know G-d. And he goes on to explain the fundamentals of scientific knowledge of creation, as well as metaphysics.
But how may one discover the way to love and fear Him? When man will reflect concerning His works, and His great and wonderful creatures,1 and will behold through them His wonderful, matchless and infinite wisdom, he will spontaneously be filled with love, praise and exaltation and become possessed of a great longing to know the Great Name, even as David said: "My soul thirsts for God, for the living God," (Ps. 42,2); and when he will think of all these matters,2 he will be taken aback in a moment and stricken with awe, and realize that he is an infinitesimal creature, humble and dark, standing with an insignificant and slight knowledge in the presence of the All Wise, as David said: "For when I see Thy heavens, the wonderful works of Thy fingers, of what use is man that Thou mayest remember him?" (Ibid. 8,4). And, in harmony with these matters, I elucidate great, general principles of the works of the Lord of the universe, so that they might serve as an opening for one who understands by which to love the Name, as some sages said on the subject of love: "Out of it thou wilt recognize the One who spoke, and the universe was called into existence."
It seems that anything that is a testable theory about reality falls into the obligation to know G-d's wisdom. String Theory is a mathematical model that attempts to better explain the behavior of matter, although it generally has not yet produced any testable hypothesis.
Actually, Rambam would call scientific principles, such as the laws of nature, angels. See The Guide for the Perplexed Part II ch. 6
They only show that all parts of the Universe, even the limbs of animals in their actual form, are produced through angels: for natural forces and angels are identical. How bad and injurious is the blindness of ignorance! Say to a person who is believed to belong to the wise men of Israel that the Almighty sends His angel to enter the womb of a woman and to form there the fœtus, he will be satisfied with the account; he will believe it, and even find in it a description of the greatness of God's might and wisdom; although he believes that the angel consists of burning fire, and is as big as a third part of the Universe, yet he considers it possible as a divine miracle. But tell him that God gave the seed a formative power which produces and shapes the limbs, and that this power is called "angel," or that all forms are the result of the influence of the Active Intellect, and that the latter is the angel, the Prince of the world, frequently mentioned by our Sages, and he will turn away; because he cannot comprehend the true greatness and power of creating forces that act in a body without being perceived by our senses.
On the other hand, Rambam explains in The Guide for the Perplexed (part II, ch. 23 (see also end of ch. 22)) that we do not consider things about the past that are impossible to prove and are inherently philosophical choices. In these areas we rely on tradition and the approach that is best morally.
Thirdly, [before choosing a philosophical model] you must be morally good. For if a
person is voluptuous or passionate, and, loosening the reins, allows his anger to pass the just limits, it makes no difference whether he is so from nature or from habit, he will blunder and stumble in his way, he will seek the theory which is in accordance with his inclinations. I mention this lest you be deceived; for a person might some day, by some objection which he raises, shake your belief in the theory of the Creation, and then easily mislead you: you would then adopt the theory [of the Eternity of the Universe) which is contrary to the fundamental principles of our religion, and leads to "speaking words that turn away from God." You must rather have suspicion against your own reason, and accept the theory taught by two prophets who have laid the foundation for the existing order in the religious and social relations of mankind. Only demonstrative proof should be able to make you abandon the theory of the Creation: but such a proof does not exist in Nature.
Evolution in the past--as opposed to current mutations--and the age of the universe might fall into this category. String Theory as a theory of creation might fall into this speculative category, but as an attempt at a unified theory of everything (joining quantum mechanics and relativity (gravity)), it is certainly good to pursue.
In summary, any theory with practical application today is advisable to pursue. But when a theory is merely a philosophical choice, we choose the one that is morally good, being that there is no practical difference. (In the popular debate between science and religion these two--science and philosophy--are often confused. It is scientifically impossible to prove--and irrelevant--that the world didn't pop into existence last Thursday. Occam's Razor is a subjective tool for choosing a philosophical model. It can be useful, but it will not always select the model that is most moral.)
I hope this helps.
In my understanding, the string theory is not about the creation of the world at all, it is about fine-tuning the explanation of the existing phenomena on a smaller, sub-subatomic scale.
All the rests are hypotheses and extrapolations that have nothing to do with the theory.
Halachicly-wise this is not different from the theory of evolution, in Rambam's approach: as long as learning the theory targets a better understanding of the Creation and the ways of G-d and making this world better (יישוב עולם) it is fine, but once it targets heresy and denial of G-d's Creation it is surely forbidden.