i thought there was a reentry permit desk in Phuket airport after you check in with your airline (as its an international airport) unless its now gone You just have to go to passport control to the left side corner booth near the Immigration office from memory if someone whos ben recently can confirm
There is a reentry permit desk at Phuket airport, but it’s not manned 24 hours, but you can always ask immigration to get someone to man it (do the permit for you).
Personally I wouldn’t take the chance and I’d go to one of the offices to get.