I would start right away with Lugol's or Magnescent iodine. One drop in his water every day. There are several posts on this forum about Iodine and also on the VWT forum.
Our dog had completely licked off the hair from his front legs and it all grew back, though I had found out he had low thyroid.
We just got a new rescue dog and I give him for now 1 drop of magnescent on a piece of hamburger and put CS in his water. The CS is since he had slight diarrhea.
Since before we got him he saw a vet, though we did not get any bloodtest results, we are planning to get a bloodtest done in the fall so we have a base and we will know how his thyroid is.