How to ask a male coworker to hangout without sounding like a creep?

I'm 19, he's 22. We work together and we generally spend about 5 hours a day alone together apart from the occasional customer or manager checking in. I thought he was adorable from the moment I met him on my first day at work.
I have his snapchat and instagram and we've been texting pretty much every night for several days. I'm 95% sure he likes me back... he makes every excuse possible to work together and take breaks together. We've bumped into each other a couple times "accidentally." He's let me wear his work jacket a few times before, and we've had some pretty real conversations.
Our manager knows there's something going on and he thinks it's cute, and he purposely schedules us together. I've talked openly with the manager; he's fine with us dating and says there's no corporate policy against it.
Should I let him take the lead and ask me out first? He's pretty shy (he was burned by his ex, who also happened to be a coworker at his former job.) Or should I just causally mention that I'm going for a bite to eat after work and would he like to join?
The last couple guys I've dated were either my age or a year younger (I was the oldest in my class, so it wasn't by choice.) I'm not sure how to proceed with a guy who's a bit older than me.
thanks in advance lol
How to ask a male coworker to hangout without sounding like a creep?
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