The whole question of time sequence in either description is questionable. Time itself was something created, and thus some rishonim (including the Rambam, Moreh Nevuchim 1:30) understand chapter 1 (at least, perhaps ch. 2 as well) as discussing a logical progression, not a chronological one. That the concept of time and chronological order only make sense after creation.

Rav Dessler writes (Michtav meiEliyahu vol II pp 150-154, “Yemei Bereishis veYemai Olam“) that not only is time a creation, the whole idea of a flow of time, that it’s a line running from past to present to future is an artifact of the human condition. And that before Eve and Adam ate from the Tree of Knowledge, people too related to time in a more complete way. Or, as our sages put it, the original Adam and similarly a baby prior to being born into a body “could see from one end of the universe to the other” — which Rav Dessler presumes includes time as well. (I gave a paragraph by paragraph summary in “Rav Dessler’s Approach to Creation“.)

Futhermore, Rav Dessler notes that the Ramban (1:3 s.v. “VaYhi Or“) not only insists that “כי הימים הנזכרים במעשה בראשית היו בבריאת השמים והארץ ימים ממש, מחוברים משעות ורגעים, והיו שישה כששת ימי המעשה, כפשוטו של מקרא — for the days mentioned in the Act of Creation were in the creation of shamayim and aretz literal days, comprised of hours and minutes, and were six like the six days of work [in a workweek]. As per the simple understanding of the scripture.” He then continues, “ובפנימיות הענין יקראו “ימים” הספירות האצולות מעליון, כי כל מאמר פועל הויה תיקרא “יוֹם”   — The internals of the matter is that what are called ‘days’ are the sephiros of emanation from above. For every statement that causes existence is called ‘day’.” As the Bahir says, this is why the pasuq says “ki sheishes yamim” — through these 6 days, 6 sephiros — “asah H’ es hashamayim ve’es ha’aretz… — Hashem made the heaven and the earth.” And the Ramban (2:3 s.v. “asher bara E-lokim la’asos“) describes the days of creation a third way: “כי ששת ימי בראשית הם כל ימות עולם כי קיומו יהיה ששת אלפים שנה — because the six days of Bereishis are all the days of the world, which will exist for 6,000 years.”

According to Rav Dessler, the Ramban also says the days of creation aren’t what we think of by days. Then again, neither are our actual days we’re living through really what we think they are. However, Rav Dessler argues, the time of creation is being described are from  before there was a human imposing our perceptions on the world. The time interval for creation, literal days, sephiros, and all of history, isn’t to be taken at face value.

For that matter, the Maharal in one of the introductions to Gevuros Hashem explains that creation is itself so alien to the human mind that nothing about is really within our ability to conceive. A more general version of what the Ramban says about time.

Also, Rashi 1:1 s.v. “Bereishis Bara“:

ואם באת לפרשו כפשוטו, כך פרשהו: “בראשית בריאת שמים וארץ, וְהָאָרֶץ הָיְתָה תֹהוּ וָבֹהוּ וְחֹשֶׁךְ, וַיֹּאמֶר אֱלֹהִים יְהִי אוֹר”. ולא בא המקרא להורות סדר הבריאה, לומר שֶאֵלו קדמו; שאם בא להורות כך, היה לו לכתוב: “בראשונה ברא את השמים” וגו’, שאין לך “ראשית” במקרא שאינו דבוק לתיבה של אחריו, כמו: (ירמיהו כו א) “בְּרֵאשִׁית מַמְלְכוּת יְהוֹיָקִים”, (בראשית י י) “רֵאשִׁית מַמְלַכְתּוֹ”, (דברים יח ד) “רֵאשִׁית דְּגָנְךָ”. אף כאן אתה אומר: “בְּרֵאשִׁית בָּרָא אֱלֹהִים” וגו’, כמו “בְּרֵאשִׁית ברוא”. ודומה לו (הושע א ב) “תְּחִלַּת דִּבֶּר ה’ בְּהוֹשֵׁעַ”, כלומר: תחילת דיבורו של הקב”ה בהושע, “ויאמר ה’ אל הושע” וגו’.

ואם תאמר: להורות בא שאלו תחילה נבראו, ופירושו: בראשית הכל ברא אלו, ויש לך מקראות שמקצרים לשונם וממעטים תיבה אחת, כמו: (איוב ג י) “כִּי לֹא סָגַר דַּלְתֵי בִטְנִי”, ולא פירש מי הסוגר, וכמו (ישעיהו ח ד) “יִשָּׂא אֶת חֵיל דַּמֶּשֶׂק”, ולא פירש מי ישאנו, וכמו (עמוס ו יב) “אִם יַחֲרוֹשׁ בַּבְּקָרִים”, ולא פירש “אם יחרוש אדם בבקרים”, וכמו (ישעיהו מו י) “מַגִּיד מֵרֵאשִׁית אַחֲרִית”, ולא פירש “מַגִּיד מֵרֵאשִׁית דבר אַחֲרִית דבר”. אם כן תמה על עצמך, שהרי המים קדמו, שהרי כתיב: “וְרוּחַ אֱלֹהִים מְרַחֶפֶת עַל פְּנֵי הַמָּיִם”, ועדיין לא גילה המקרא בריית המים מתי היתה. הא למדת שקדמו המים לארץ. ועוד, שהשמים מאש ומים נבראו. על כרחך לא לימד המקרא בסדר המוקדמים והמאוחרים כלום.

Rashi says that in the straightforward explanation, “the scripture did not come to tell us the order of creation, to say that these came first.” As Rashi notes, we could have asked a question related to yours about water. We are never told when water was created; its existence (as well as darkness, Hashem’s “Spirit”, shamayim and aretz [left untranslated intentionally]). “Perforce you must [conclude that] the scripture doesn’t teach anything about the order of earlier and later.”

On Bereishis 2:4 s.v. “Soldos haShamayim veHaaretz beHibar’am beYom Asos Hashem“, Rashi writes two comments. The second is homoletic (about how the world was created with the letter hei), but the first addresses the verse saying “These are the consequences of shamayim and eretz when they were created on the day The first is “למדך שכלם נבראו בראשון — to teach you they were all created at the beginning.

Which would seem to mean that while the first Rashi just says the Torah doesn’t tell us the order in which creation occurs, this Rashi is saying there was in fact no chronological order at all. Which would explain how chapter 1’s week is all one day in chapter 2.

This is in addition to the question of what if anything happened before Bereishis 1:2. The creation and destruction of worlds described in Bereishis Rabba. Or the Ramban’s description of a gap between the creation of matter in 1:1 and Hashem giving it the forms we know today in the rest of the chapter. (See my general survey “Different Approaches to Creation“.)

In short, the insistence in some circles of Orthodoxy today that these verses must be taken literally are more the product of counter-reformation than tradition. It is a reaction to the many outside Orthodoxy who question the historicity and literalness of far more of our Torah. Our most quoted rishonim do not presume six literal days, or even the same sequence stretched over longer eras. Non-literalism, or at least not insisting on literalism, is actually the mesoretic choice.