Maybe he’s too young now but many kids like climbing in general so soon you might be able to go climbing together :)

Exactly, and the only way to one day be actually have teenage kid(s) to share the joy of climbing with, is to have earlier looked after young kids that weren't ready yet to go climbing. ;) OK, some people may say when they're teenagers they'll just want to "hang out at the mall" but I suspect some things, like e:g rock climbing, or making music, are potentially still very cool to teenagers even when being done with parents. (Disclaimer, ours are still young, so yet to see if they'll want to do that later, but their level of interest in the outdoors and music is highly promising so far...)

Maybe all you need is one more year. I'm bouldering with my 4yo weekly :)