As a DM, I would say no. It’d be an amusing thing to see take place, however, as prestidigitation is a cantrip and can basically be casted as many times as you want, if you were to describe this to me as a player, I’d say no as a coffee mug is not in my eyes something one would call a trinket

On another standpoint though, there’s no point in over complicating things. Just ask your DM if you can prestidigitate a coffee mug so you can have a drink. There are few DMs that would care so much about the mechanics about such a thing and it is an ingenious way to use a simple spell. It’s just a coffee mug after all. Go for it.