If you actually know someone and you really want to tease that out you don't ask them, first you invoke nostalgia organically, then when you're both tripping down memory lane you offer up your own favourite thing from recess in primary school (starting fires with a magnifying glass, say) and wait.

More often than not they'll gift back a similar story of their own.

I'll respond to your intended meaning of "getting to know someone" instead of knowing. First, 'sounding like a tryhard or weirdo' is a judgement call you make. if you suspect that is how you'd sound, of course that is what you will think others will perceive. Second, you don't need to force it; nothing in this advice says "ignore all semblance of conversational flow." Thirdly, and more directly, people will only distrust you if they detect you are insincere. There's so much more to communication than words. People appear as not-quite-right even with eloquent speech; people can appear sharp while speaking very simply. This is because it isn't in the words. It's hard from the analysis of this webpage to evoke the feeling of desiring to connect with someone, which is the whole point in the first place. That feeling, which is just you honestly enjoying human interaction, is sufficient for avoiding appearing as a tryhard or anything like that, because it is just you acting honestly.