Yeah. In (short) retrospect, the thing that we're responding too -- the engineer who suggests we should ask them out for coffee -- is a bit strange and maybe missing context. I'm guessing during the interview, the question felt like it was asking for a concrete example, perhaps in a situation where coworkers have worked together for some time. I'd be surprised if anyone's idea of a good activity, when first joining a workplace, is: "Yeah ask me out to coffee and what I feel about being a _____ at my new company".
Treat them like they already belong.
As for it-might-look-like-a-date ... ask them to tag along for your mid-day coffee run. Don't ask them out for coffee on a Friday evening.