Isn’t dating how you can get to know her?
If you’re talking to someone new (in person) and you think there’s a connection there, why not suggest an activity right then and there? E.g. “Hey, I was planning to hit that jazz festival sometime this weekend. Feel like coming along?” Stay away from trite things like dinner and a movie which signal “date.”
Don’t frame it as a date—just buddies, no pressure. In contrast, calling her on the phone introduces artificiality and pressure to it…now you have to think of clever things to say, explain why you couldn’t have asked her out when you saw her, yadda. And you get so much more info from seeing the expression on her face than you would on the phone, either encouraging you to go for it or to desist.
But I think the reality is like the Viet Nam War. “No, we’re not having a war here!” Like hell. You’re out with her, getting to know her, not committed to her and you may mention something that’s a deal-breaker for her or vice-versa. Or it may turn out that you have more and more in common and it naturally morphs into something romantic.
Most importantly, even if nothing romantic transpires on this “not a date,” you get your hat in the ring. And you do this before someone else snaps her up…get in contention at least.
JMO YMMV.
Given the details of the OP I wouldn’t automatically be concerned about the age diff. Some 22 y/o’s are pretty mature and you yourself seem pretty immature ( I keed, I keed!) so maybe you’ll meet in the middle.