We have Epstein's emails, but they do not go back to 1985-1988, when this could have happened. The reason is obvious, few people had email back then. We do know that by the time Epstein got email, he and trump had been friends for a long time.
In 2002, trump claimed he had been best friends with Epstein for 15 years, so starting in 1987. That is a general number, so it could easily have meant in 1985. We know that in 1987, Epstein was bringing underage girls into trump's casino with trump's consent.
The timeline works.