IME of a year of OLD and a fair bit of casual sex, no man will voluntarily discuss contraception unless you being it up.
I'm in my early 50s, so the chances of pregnancy are low, but I still have periods, so they're not non-existent. I don't use any LARC, so realistically condoms are the only option.
If I'm prepared to fuck them with no condom, I'm probably prepared to fuck others with no condom - and they do often ask how OLD has been going, so they know they're not that dpecial or exclusive. Plus men my age, like me, would have been going through puberty at the height of the AIDS epidemic, when condoms were everywhere and we were all going to die from unprotected sex. Not one of them mentions using condoms or having had STI tests before I bring it up. Also men, if you're shagging around, one STI test a year with your work's private health provision isn't enough.
Most of them will use a condom if I insist, though some of them will whinge mightily about how sex with condoms just isn't as good, and do they really have to... no, they don't have to, but I don't have to have sex with them. If using a condom means they can't sustain an erection, they won't be getting a return invitation anyway (see also: Viagra.)
If you give them any leeway, they will not use a condom. There is a distinct lack of logic, too. If you insisted on condoms first time, why would they suddenly not be required the second time, when you've had no time to get the pill or an STI check? For me, if I ask for condoms to be used, I expect it for that whole of that session - every time there's penetration, there should be a condom, not just the first time. I usually have a good stash of condoms available because I would expect them to "forget" or just hope for it without.
Men are really shit about using condoms, especially the ones who are more likely to sleep around. Yes, I also prefer sex without condoms, but I also prefer sex without STIs.
You need to overtly mention condoms (and probably provide them) every single time - if there's any chance a man can have sex without one, he will.