Chapter 24 which starts וְאֶל־מֹשֶׁ֨ה אָמַ֜ר עֲלֵ֣ה אֶל־י״י֗ according to Rashi took place before the events of Matan Torah in Yisro. Rashi says פרשה זו קודם עשרת הדברות. בארבעה בסיון נאמר לו: עלה. Then 12 pessukim later when it says וַיֹּ֨אמֶר י״י֜ אֶל־מֹשֶׁ֗ה עֲלֵ֥ה אֵלַ֛י הָהָ֖רָה וֶהְיֵה־שָׁ֑ם וְאֶתְּנָ֨ה לְךָ֜ אֶת־לֻחֹ֣ת הָאֶ֗בֶן וְהַתּוֹרָה֙ וְהַמִּצְוָ֔ה אֲשֶׁ֥ר כָּתַ֖בְתִּי לְהוֹרֹתָֽם, Rashi says it took place לאחר מתן תורה. According to Rashi, the timeframe of the parsha jumps back and forth from before Matan Torah to Matan Torah in Yisro to the end of the parsha going up the mountain and after that the beginnig of Mishpatim. The Ramban is not happy with this and learns the parshios are in chronological order. According to the Ramban the aseres hadibbros were given with all of the mitzvot and the next day Klal Yisrael affirmed their acceptance of the mitzvot and Moshe went up the mountain for 40 days.
According to the Ramban the words of נעשה ונשמע said in possuk 7, וַיֹּ֣אמְר֔וּ כֹּ֛ל אֲשֶׁר־דִּבֶּ֥ר י״י֖ נַעֲשֶׂ֥ה וְנִשְׁמָֽע are meant to say that Klal Yisrael accepted the Moshe's relaying of the commandments is accurate and we accept all commandments that come from Hashem. According to the Ramban, we don't have Tosfos's question (Shabbos 88a) of why was there a need to put the mountain over Klal Yisrael's head if they said naaseh vinishma, because the mountain over the head at the aseres hadibros preceded the statement of naaseh vinishma.
Possuk 3 says וַיָּבֹ֣א מֹשֶׁ֗ה וַיְסַפֵּ֤ר לָעָם֙ אֵ֚ת כׇּל־דִּבְרֵ֣י י״י֔ וְאֵ֖ת כׇּל־הַמִּשְׁפָּטִ֑ים וַיַּ֨עַן כׇּל־הָעָ֜ם ק֤וֹל אֶחָד֙ וַיֹּ֣אמְר֔וּ כׇּל־הַדְּבָרִ֛ים אֲשֶׁר־דִּבֶּ֥ר י״י֖ נַעֲשֶֽׂה. What was accepted here and why did they not say ונשמע? Rashi says את כל דברי י״י – מצות פרישה והגבלה. ואת כל המשפטים – שבע מצות שנצטוו בני נח, ושבת, וכיבוד אב ואם, ופרה אדומה, ודינין, שנתנו לו במרה (This is slightly different from what Rashi says in Beshalach (15:25) that in Marah they were given שַׁבָּת וּפָרָה אֲדֻמָּה וְדִינִין and he omits כיבוד אב ואם, why does he switch? See Toras Menachem Vaeschanan 5628.) According to Rashi it would seem the נעשה said here is that Klal Yisrael accepted these commandments given to them while 4 pessukim later the נעשה ונשמע is past of the event of the bris and is the prelude to the acceptance of the commandments of Hashem. However, according to the Ramban, why does the terminology change? In the Ramban's commentary he explains the possuk in the same vein as the possuk of נעשה ונשמע but doesn't seem to fully address why does the possuk change terminology? The Kli Yakar suggests they first accepted all the mitzvot that they heard. When the people saw the splitting of the blood they took it as a simple that only half the mitzvot have been said and their will will be more mitzvot given and they said we accept those upon ourselves as well.
Possuk 4 says וַיִּכְתֹּ֣ב מֹשֶׁ֗ה אֵ֚ת כׇּל־דִּבְרֵ֣י י״י֔. The Eben Ezra says אחר שספר להם כל דברי השם המצות והמשפטים כתבם, וזהו: ספר הברית. This is the approach of the Ramban that this happened after the giving of all the mitzvot from Yisro and onward. The point of the writing was to record the mitzvot that were given. Rashi however, says וַיִּכְתֹּב משֶׁה. מִבְּרֵאשִׁית וְעַד מַתַּן תּוֹרָה, וְכָתַב מִצְווֹת שֶׁנִּצְטַוּוּ בְמָרָה. Why does Rashi say that Moshe wrote from בראשית until their resent moment, why not learn that Moshe wrote the laws and description Hashem gave in the lead up to Sinai? And why does Rashi use the word וכתב in the middle, just say מִבְּרֵאשִׁית וְעַד מַתַּן תּוֹרָה, וְמִצְווֹת שֶׁנִּצְטַוּוּ בְמָרָה? Rashi can't learn like the Ramban for he holds that this parsha is before the giving of the mitzvot. According to Rashi this is in the parsha of the bris. The point of the writing is to give strength to the bris between Hashem and Klal Yisrael. That is why Rashi understands that the entirety of the Torah is written for it gives the picture of the entirety of history being for the sake of Klal Yisrael. Rashi splits two different acts of כתיבה since the parshios of the stories of the Torah are a storyline and would be written as the way it is in the Torah but the mitzvot of Marah could not be written in the same form as a written parsha of Torah because the details expressed in the Torah were not given yet. That is why Rashi says מִבְּרֵאשִׁית וְעַד מַתַּן תּוֹרָה was written as Torah כָתַב מִצְווֹת שֶׁנִּצְטַוּוּ בְמָרָה, and he wrote the מצות, it was a writing of laws given at Marah but not as parshios of the Torah (Likutay Sichos volume 21.)
What exactly is entailed for kabbalas hamitzvot and if it is not present if the gerus is valid or not has been debated over the past few centuries, see a summary of the shitos, in hakirah and toraland.
The opinion of the Ramban (Yevamot 45b) is that kabblas mitzvot is an integral role of the gerus process that needs the Beis Din to be present at the time of the ger's acceptance of the mitzvot and without it the gerus is invalid. The Rambam in his presentation of the steps necessary for gerus (Issuray Beah 13:4) says וְכֵן לְדוֹרוֹת כְּשֶׁיִּרְצֶה הָעַכּוּ''ם לְהִכָּנֵס לִבְרִית וּלְהִסְתּוֹפֵף תַּחַת כַּנְפֵי הַשְּׁכִינָה וִיקַבֵּל עָלָיו עֹל תּוֹרָה צָרִיךְ מִילָה וּטְבִילָה וְהַרְצָאַת קָרְבָּן., he does not mention kabbalas mitzvot. There is a debate in the Achronim as to if the Rambam holds that קבלת מצות is מעכב as noted in the articles above, but it would appear he does not hold it is part of the gerus process.
Rav Yehuda Amital suggests that this debate has its roots in the gerus process which occurred at Matan Torah. The Ramban at the end of Emor (24:10) seems to hold that even pre Matan Torah there was a concept of having laws and the status of a Jew. So what was the gerus process that was completed during the bris in this week's parsha (see Krisos 9a)? What was added was the obligation of mitvot. That is why the Ramban holds there must have been mitzvot given before the event of the bris because the acceptance of mitzvot is the entire essence of the gerus. There had to be mitzvot that were accepted! On the other hand, if we assume not like the Ramban, as he himself notes, the French Rabbi's disagreed with him, then the gerus of Matan Torah was not a mere acceptance of the Torah, but establishing a שם ישראל, a Jewish nation and than doesn't require a kabblas mitzvot. Instead the mitzbot become obligatory because one is a Jew. So he can learn the order of the parshios in the way Rashi understands which is the simple read of the Gemarah as noted by the Netziv here. In other words, according to the Ramban an act of gerus, becoming Jewish is accepting mitzvot as then one is joined to the Jewish nation. According to the Rambam, one accepts to be a Jew and therefore, one is obligated to keep the mitzvot.
It does behoove an explanation as to why according to Rasih the parshios are out of order. Furthermore, why does Rashi change his terminology, in possuk 1 he says, פרשה זו קודם עשרת הדברות and in possuk 12 he says לאחר מתן תורה, why change from עשרת הדברות to מתן תורה? The Rebbe explains (Likutay Sichos volume 26) that there are two things that happened at Matan Torah. There is a giving of laws that must be accepted and then there is the event of the covenant between Klal Yisrael and Hashem. The parsha of Yisro lists the mitzvot as commandments and hence other mitzvot follow. Only following that does the Torah focus on the bris of Sinai. This is alluded to by the change in Rashi's terminology. The parsha of the bris is said before the עשרת הדברות, before the giving of mitzvot, of that aspect of Matan Torah . It is the commandments that precede this parsha. After the bris Rashi refers to the event with its total name, which is מתן תורה.