Normally it would be very possible and quite easy. The problem here isn't VAPI, it's Calendly -- it's difficult to do in any "normal" way because the Calendly API does not allow you to book appointments. No, I'm not kidding -- look through their API docs and you'll see what I mean. I think I've seen that some enterprise customers are given access to an endpoint to do that, but anyone else, nope... The only way I've seen of doing it is quite "hackish" -- e.g. using something like Selenium to click through an actual booking page (e.g. simulating a human). Not ideal and could break easily if the formatting or structure changes. I usually work on Retell, not VAPI, and over there we use cal.com instead for this use case.