This one is different. I not only think they have sex during NGE, I think we witnessed part of it, and heard another part unknowingly.
It would be nearly impossible to convincingly summarize this theory in text or image form, which is why I made a video drawing on the necessary footage.
Here's something interesting.
In between episode 9 (the day of the "This is the impenetrable wall of Jericho!" line) and 15 (the night of the alleged sex), there are 7 days, as far as I can tell. An extra day passes after the line during episode 9, then each episode till episode 15 seems to have one dawn and dusk.
Here's the biblical fable of Jericho.
Then the Lord said to Joshua, “See, I have delivered Jericho into your hands, along with its king and its fighting men.
March around the city once with all the armed men. Do this for six days.
Have seven priests carry trumpets of rams’ horns in front of the ark. On the seventh day, march around the city seven times, with the priests blowing the trumpets.
When you hear them sound a long blast on the trumpets, have the whole army give a loud shout; then the wall of the city will collapse and the army will go up, everyone straight in.”
I don't know about trumpets, but Asuka seemed impressed enough by Shinji's violin. She kissed him right afterwards.