I know it might be a problem with someone who has social anxiety but also taking the lead in making an overture of friendship often has great results.
Let's say you like airplanes and in a conversation an acquaintance mentioned they like airplanes too. If you paid attention to it you might remember it when you see an air show is coming to town and take the first step by asking them if they'd like to go with you.
Worst which can happen is that they are busy that day, so nothing personal
I know some people are afraid of rejection but unless you take a risk you won t find out if that person might be a friend (and who knows, maybe they are shy too and were afraid to make an overture of friendship).