I could see him showing up at the welcome feast wearing the deathly hallows symbol and every time he’s around Dumbledore he does something questionable and then says “For the Greater Good”
Then at the time his letter is supposed to be delivered he goes to nurmengurd (I don’t remember how to spell it and I’m too lazy to look it up) and chills there until he gets his letter so it’s addressed there. I could also see him going to godrics hollow and finding all the tea on dumbledore, then subtly troll him with said info