Our Sages in Yevamot 46b and Keritot 9a in the Bavli say that the requirements for a proper conversion are bringing a sacrifice, Mila, Kabalat Hatorah and immersing in a Mikvah.
The Gemara in Yevamot 46b understands that Bnei Israel converted at Maamad Har Sinai: sacrifices were brought (Shemot 24:5), Mila was performed in Egypt before leaving in order to perform Korban Pesach (Kol Bo comment on Yechezkel 16:7 from the Pesach Haggadah), Kabalat Hatorah at Matan Torah, but what about immersing in the Mikvah?
When, where and how did this happen? How about the Jewish ladies after Matan Torah immersing after being Niddah? And the other mitsvot that require immersion?