There’s a law of פולטת שכבת זרע- If semen comes out from woman’s body after intercourse, it contaminants her. The source is from מתן תורה where days before were forbidden in intercourse. The reason was to ensure that no woman would be tamei if she discharged the semen right before the Torah was given. By refraining from intercourse for a few days before, it ensured that any woman could go to the mikveh the night before Matan Torah and that no semen would make her Tamei afterwards. After a few days, the semen loses its stays bc it spoils in the womb.

There are four opinions on the timing of this law. Everyone agreees Matan Torah was on Shabbos morning. a. R elazar says the time of separation started on Thursday. For two days, semen can make tumah, but not on the third day. b. R yishmael says the time of separation began on Wednesday. We learn that semen can make tumah for three days, but not on the fourth day. c. R akiva says the time of separation began at dawn on Wednesday so there a full 60 hours until they went to mikveh for Matan Torah. These first three opinions all hold that the women went to the mikveh on Friday night bc it wouldn’t be proper to go Shabbos morning. It’d be better that all the Jews march in unison to Matan Torah. d. The rabanan hold the separation began wed at dawn and that they went to the mikveh Shabbos morning. A full 72 hours passed between potential intercourse and time of tevilah.

We see from this discussion that the only issue was women would be tamei at Matan Torah from פולטת שכבת זרע, but it was fine is they were טבולי יום at the time. Certain vestiges of tumah remain after tevilah until the next nightfall, but those remains of tumah did not preclude the tevul Yom from being at matan torah. (Practically, women also toiveled on Friday afternoon and did not have semen emerge from their bodies and weren’t even tevul Yom at Matan Torah, but the point is that it could have happened. Had semen came out before Friday night, they would have immersed again Friday night)

The Torah was given during the day specifically bc “HaShem did not give the Torah in secret.”

This whole discussion is all when semen emerged from woman’s body, (the heat of the body spoils the semen) but semen that came out from mans body and was lying around has tumah as long as it’s still moist.

The Gemara is unsure if jewish semen in non Jewish woman spoils as quickly. Maybe Jewish bodies are “warmer” bc of nervousness to perform Mitzvos or non Jewish bodies are also warm bc they add crawly creatures. The gemara is certainly unsure about Jewish semen in an animal.