You’re correct in not jumping to sex for something long term but also realize that for women, that is what they’ll try and use to lock you down.
If she thinks you’re a catch she will try to initiate sex to lock it down. Seen that too many times.
My thing is to try an initiate/tease at intimacy somewhat early on. If she’s fully shutting it down, then you know how to move accordingly.
Not a one size fits all but there are patterns.
Story was a bit vague but I didn’t see anything indicating him trying to smash on the first date.