Generally we assume that God is omnipotent, and could have created the world in a single day/act, so He must have had a reason to organize creation into 6 days. Why?
In other words:
there are many answers as to why not in one saying. here's one possible answer: "By ten divine sayings the world was created. Could it not have been created by one? What does this teach us? In order to emphasize the guilt of the wicked who destroy the world that was created with ten sayings and the merit of the righteous who preserve the world that was created with ten sayings." avos ch.5 (i.e. to give the righteous more reward since they are sustaining a world created with more "work")
The ten divine sayings correspond to the ten sefirot in kabala.
As for why specifically seven days, see this: http://www.dafyomi.co.il/parsha/breisht3.htm
In fact, everything was created in the first instant of the first day, and only through the other 7 days was everything revealed / placed in its proper place.
Besides for looking at the commentary of Rashi throughout the first few chapters of Bereishis, take a look at this very interesting paragraph from the Maamer (ספרי כ"ק אדמו"ר > מאמרים מלוקטים > חלק א > בס"ד. יום ב' דראש השנה ה'תשמ"א):
הנה ביום הראשון דמע"ב (כ"ה באלול) נבראו השמים והארץ וכל צבאם מאין ליש כמ"ש12 בראשית ברא אלקים את השמים ואת הארץ, שהשמים והארץ וכל צבאיהם (את השמים לרבות תולדותיהם ואת הארץ לרבות תולדותי'13) נבראו אז מאין ליש. דגם הנבראים שנתהוו בהימים דמע"ב שלאחרי היום הראשון הרי אז היתה התגלות שלהם, יצירה ועשי', אבל בריאתם מאין ליש היתה ביום הראשון14. וגם האדם, שהמעלה דראש השנה היא (כנ"ל) שביום זה נברא האדם, הרי כתיב בי' וייצר ה' אלקים את האדם עפר מן האדמה15, והעפר מן האדמה (שממנו נוצר גוף האדם) נתהווה ביום הראשון. ובמיוחד ע"פ הידוע16 שהכתוב בראשית גו' מדבר בהתהוות השמים והארץ הגשמיים וגם בהתהוות האצילות, בראשית חכמה, אלקים בינה, את השמים ז"א ואת הארץ מלכות. וכל זה נתהווה ביום הראשון. וגם איתא במדרש עה"פ ויהי ערב ויהי בוקר יום אחד17, דמ"ש יום אחד (ולא יום ראשון) הוא לפי שבו הי' הקב"ה יחידי בעולמו. והיינו דההתהוות דיום הראשון היתה באופן שהי' אז נראה ונגלה שהוא ית' אחד בעולמו18. וענין זה (הקב"ה יחידי בעולמו) הי' אז מצד למעלה ומצד וכמו שנמשך למטה, והמאמר שנאמר ביום הראשון הי' ויאמר אלקים יהי אור19, שעל ידו יוכלו בנ"י (ע"י עבודתם) להאיר את העולם כולו ולגלות את הפנימיות שבו, אוא"ס שלפני הבריאה והצמצום, ועד לעצמות ומהות, שבהעולם כמו שהוא מצד עצמו (גם כמו שנברא ביום הראשון) הוא בהעלם. וי"ל דזהו שאמרו רז"ל20 אור שנברא ביום ראשון לא הי' העולם כדאי להשתמש בו, והבדילו לעצמו21, כי אור זה הוא למעלה מהעולם, ובפרט ע"פ המבואר בכ"מ22 הפירוש (וגודל העילוי) דהבדילו לעצמו.
12) בראשית א, א. וראה רמב"ן עה"פ: ואין אצלנו בלשון הקודש בהוצאת היש מאין אלא לשון ברא.
13) פרש"י עה"פ שם, יד.
14) פרש"י שם ובפסוק כד.
15) בראשית ב, ז. והיינו, דגופו של אדה"ר לא נברא ע"י מאמר אלקי בפ"ע [כשאר הברואים], ועשה וייצר את האדם בהעפר שהי' מקודם (תו"ח בראשית יט, ב).
16) ראה זח"א לא, ב (בתוספתא). רנו, ב. וראה ד"ה בראשית ברא תרנ"א (סה"מ תרנ"א ע' פט ואילך).
17) בראשית א, ה. ב"ר פ"ג, ח. פרש"י עה"פ.
18) המשך תער"ב ח"ב ע' תתקצח. סה"מ תש"ד ע' 222. ושם, שזה למעלה גם מהמציאות דאצילות.
19) בראשית א, ג. וראה בהמשך תער"ב ובסה"מ תש"ד שם, השייכות דאור שנברא ביום ראשון לענין "הקב"ה יחידי בעולמו".
20) שמו"ר רפל"ה. וראה בהמצויין בהערה הבאה.
21) מדרש תהלים עה"פ תהלים כז, א. ירושלמי ברכות פ"ח ה"ו. ב"ר פ"ג, ו וביפ"ת שם.
Basically, it quotes Rashi as saying that everything was created on the first day, only revealed later, then it goes on to say even the body of the first man (who was seemingly created specifically on the 6th day, Rosh Hashana (and that's the whole point of Rosh Hashana as mentioned earlier in the Maamer), was created on the first day (only his soul was blown in later), since it was made from the dust which was created on the first day.
Then he says that not only was the physical heaven and Earth created on the first day (meaning not only the spiritual worlds ("physical heaven") where the angels and souls are etc.. was created on the first day), but even the world of "Atzilus" -- which is a state of being which is even greater than all of the heavens, was created on the first day.
So basically, everything that exists (and beyond) was actually created on the first day.
As to your question: why did he split it up into 7 days? See here which explains how Hashem used 7 "Sefiros" to create the world, so it had to be in 7 days, one day for each Sefirah.
On the one hand the Sages tell us that the world was created with ten qualities1 and ten utterances2—which the mystics understand3 to correspond to the ten sefirot.4 This explains why ten is considered a "complete" number.5 Examples: a) Every physical object comprises three dimensions. Each dimension is composed of a beginning, end and body. Together with the space it occupies, every entity has ten components. b) A person's life is divided into decades; each decade with a unique theme.6 c) A quorum of ten is needed to constitute a minyan.7
On the other hand, we find other sources that speak of G‑d creating the world with only the final seven8 sefirot.9 This is why the world was created in seven days—each day corresponding to one of these spiritual tools, and the creations of each day are a reflection of the divine attribute that dominated on that particular day.
So if there are 10 Sefiors in reality, why wasn't it created in 10 days? He explains more in the article, but I've quoted the direct answer: .....
The same is true of the divine sefirot. Directly involved in the creation of the world are only the seven emotional traits. But G‑d's Wisdom, Understanding, and Knowledge are heavily invested in creation,10 albeit in a more concealed and indirect manner.11
here are the notes / sources from that article
Talmud Chagigah 12a.
Ethics 5:1.
See Midrash Shmuel on Ethics ibid.; Zohar II 42b ff.
The fact that the first three sefirot, the intellectual faculties, are also involved in creation is also evident from Sefer Yetzirah (1:1), "The world was created by three: ...the Book, the Scribe, and the Narrative." Chassidic teachings (see e.g. Ushavtem 5634) explains this as referring to Chochmah, Binah, and Da'at.
Since the Torah is the blueprint of all creation (see below, footnote 10), the fact that the world was created with ten tools (which results in ten being a "perfect" number) is because the Torah itself is rooted in the Ten Commandments.
Ethics 5:22.
See Likutei Sichot vol. 30 p. 2 ff.
In many of the sources, it speaks only of six Sefirot—i.e. Chesed through Yesod. This is because the final sefirah, Malchut, possesses no distinctive quality; its function is to absorb the energies of the higher six attributes and use them to actually descend and create—and "reign" over the created entities. (Malchut is often compared to the moon, which merely reflects the light of the sun.)
See Zohar I 3b, 15b, 247a.
This is why the Zohar (vol. II 161b) tells us that the Torah is the blueprint of creation: "G‑d looked in the Torah and created the world." This is because Torah is G‑d's intellect, which is the source of (the midot that create) the world.
The primary ideas expressed in this response are taken from Maamar Isa B'Midrash Tehillim.
The world was created in 7 days because that makes it the kind of world that fits man who is nivra be'tzelem.
I.e. man expects a particular graduality of completion which is now the way the world works.
Therefore sheshes yamim taavod and bayom hashevii Shabbos.
The premise of the question is correct: God's omnipotence rules out the possibility that He was unable to complete creation instantaneously. Therefore it would seem that He did it in this way not because He had to, but rather to teach us something, to demonstrate certain concepts that relate to the number 7 (and using a day, which is a full cycle, is a more effective way to symbolically indicate separate significant/complete units of time than, say, 7 minutes). Here are two possibilities, both pertaining to Shabbos:
1) The Mekubalim write that each day God imbued creation with one of the seven lower Sephiros, culminating in Shabbos with the introduction of Malchus (the last and highest of the seven. I don't recall the exact source for this idea).
2) The Maharal in Tiferes Yisrael (chapter 40, and in other places in his writings) writes that the number 6 represents physicality ('geshem') because the physical world has 6 directions/sides: up, down, and 4 directions. The center of the 'box' is spirituality and holiness, symbolized by the number 7. In his commentary to Pirkei Avos (Derech Chaim Chapter 5 mishna 15) he further develops this idea and writes that 7 represents specifically the connection of the holy to the physical: 10 represents pure, ethereal holiness, 4 represents total physicality, and 7 is in the middle - it's the bridge between both extremes.
In other words, the number 7 refers specifically to holiness that is located inside the 'box' of physicality and that relates to physicality, as opposed to a holiness that is detached from the physical aspects of this world. So too Shabbos symbolizes the connection of holiness to corporeality - symbolized by the fact that it is the seventh day.
So, in summary: 1) To show that the seven sephiros are inherent in the creation, and that Shabbos is connected to the seventh, which is Malchus. 2) To show that Shabbos symbolizes the linking of holiness to physicality.
(For more on the significance of the number 7 in general, see the Collected Writings of Rabbi Samson Raphael Hirsch vol. 3, starting from page 97, where he discusses at length the number 7 in various contexts in Judaism.)
