In the Torah portion Beshalach (Shemos 16,8) it says that the Jews were to receive meat at night:
וַיֹּאמֶר מֹשֶׁה בְּתֵת יְהוָה לָכֶם בָּעֶרֶב בָּשָׂר לֶאֱכֹל וְלֶחֶם בַּבֹּקֶר לִשְׂבֹּעַ - And Moses said when Hashem gives you in the evening meat to eat and bread (i.e manna) in the morning.
It then says that they received the meat shemos 16,13-14:
וַיְהִי בָעֶרֶב וַתַּעַל הַשְּׂלָו וַתְּכַס אֶת הַמַּחֲנֶה וּבַבֹּקֶר הָיְתָה שִׁכְבַת וַתַּעַל שִׁכְבַת הַטָּל וְהִנֵּה עַל פְּנֵי הַמִּדְבָּר דַּק מְחֻסְפָּס דַּק כַּכְּפֹר עַל הָאָרֶץ.
הַטַּל סָבִיב לַמַּחֲנֶה.-and it was that evening the quail (type of bird) came up and it covered the encampment and in the morning there was a layer of dew and it evaporated and behold there was manna.
So we see that there was quail meat that required shechita.
Now let us go to the laws of converts in Yevamos 46a - b
אמר ר' חייא בר אבא אמר ר' יוחנן לעולם אין גר עד שימול ויטבול וכיון דלא טביל נכרי הוא - a person isn't a convert until he is circumcised and ritually immerses. (we are commanded to circumcise in Bereishis ובן שמנת ימים ימול לכם כל זכר לדרתיכם- eight days old shall you circumcise for future generations)
באבות נמי טבילה הוה מנא ליה
- How do we know ritual immersion happened with our fathers
מהכא (שמות כד, ח) ויקח משה את הדם ויזרוק על העם וגמירי דאין הזאה בלא
טבילה - From here (at Mount Sinai just before accepting the Torah) "and Moses took the blood and threw it on the the people" and we have a tradition that there is no sprinkling without ritual immersion.
From here we see that before the giving of the Torah the Jewish nation were not Halachicly Jewish until they immersed and their slaughtered animals were treif (which they cooked in their pots). Source: שחיטת נכרי נבילה slaughter of a gentile is a neveila (treif) (Chulin 13a)
So since they used their pots for cooking quail that was neveila every night, As soon as They converted at Mount Sinai, they needed to wait 24 hours in order to use their pots which they had used for treif meat when they were gentiles, so that the taste in the walls of the pots became pagum(see Nazir 37b) - unfit for purposes of consumption and permitted Min hatorah to use for the kosher meat which they ate henceforth.