In a kinda similar boat, though less "trying to convince" and more "trying to decide if we want a kid". (Because really, the boat for multiple kids for us has sailed.) My wife's five years younger, but we only met three years ago, so it feels like we've been speed-running our relationship while simultaneously dealing with life and career stuff.
I live across the country from my nephew, but if I end up not having kids, he can look forward to notably more visits and funtime with the uncle.
I think it's more like start early > start late > start never. There's more hurdles, and less chance of success - but I definitely wouldn't say it's a bad idea. The worst that happens is nothing happens. I sincerely hope you two at least try. Good luck.
The risks of childbirth for a healthy woman, even 40+, are negligible. And the worst of issues for the child, like Downs, can be screened for with perfect accuracy. The most difficult part with aging is actually getting to the point of childbirth!
I also would emphasize that it's not like not having a child is without issues. Much of the West, including the US, is already suffering with from increasing isolation, depression, and other such issues. And aging, especially without family, is likely to only exasperate these issues. Friends that will last forever, don't. And it becomes more and more difficult to meet new people as you age. Places like Japan and South Korea may be a foreshadowing of where we're headed, and it's not pretty. See things like kodukushi - lonely deaths. [1]
You've just made me think it would be a bad idea anyway at this point :(.
Oh well, at least I have many nieces.