What do you do after you’re rejected by someone?

As in how do you treat or act around them, or do you avoid them entirely?

Recently got rejected by someone I confessed to, but they said they thought I was cool and would like to hang out sometime. We weren’t already friends (more acquaintances) when I asked them out, but I haven’t seen much in terms of initiative to materialize their words.

So now I’m wondering if their desire to be friends was more of a way to assuage the sting from rejection than a genuine desire. Of course no one can answer that for her, but I was just curious how others handle rejection. Like do y’all just give up and walk away from the person entirely or perhaps something different?

clarity edit: I don’t intend on forcing anything. I see her regularly and we chat about random stuff, but I’m not actively pursuing the friendship she proposed. This approach is new to me, so I was curious if I was being too “cold” or acting disinterested. I know I’m not—I’m merely matching her energy.