For dating apps, how do you offer a new date/time for a first date without losing frame when the first date/time doesn't work with the woman's schedule?

This is assuming that the woman is actually a super busy person (med student in residency or something like that)

My approach was to essentially say "no worries, how about x day instead"

But it seems impossible for a guy to not come across as being too available with that. Is there a RP way of responding to the time conflict that isn't just giving up?

Seems like all the previous advice is that if they don't offer a new time, then you should next, but idk, it seems like a gray area if you're getting along well with the person (at least through an app)