I haven't grown thyme before (will do this year.) but I did with an indoor rosemary which I started two years and still have it to this day. I'm sure others here will chime in about thyme.

Rosemary's easy herb (once you get it established). Do you insert whole (rosemary and starter pot) in a terra cotta pot? If so, try to cut up the starter pot first before potting it. You can do it anytime you'd like, there is no real risk if you're inserting a small pot in large pot. Unless the rosemary is so fragile that you can break it by shaking the pot as you try to insert it, in that case, wait a bit.

I used a peat pot and the rosemary's roots didn't go through it when I re-potted. Rosemary likes it little on dry side so that might be why the peat pot didn't break down enough for roots to break through. Hence cutting the pot up to make it easier for roots.

Little advice: Be careful if you're not using a supplement light directly above your rosemary. My indoor rosemary were angling toward my window and I didn't rotate or support it back then so it were shaped like half c. Oops. I set it outside during summer and it does much better so I suggest you do same.

How would you suggest cutting up the starter pot (the herbs are already been potted in them and have sprouted)? Just carefully cutting bottom off so the plant can grow directly in to the soil in the terra cotta pot?

Thank you for responding.

First, is your starter pot a peat pot or cow pot that's designed to break down and become plant food when you place it (with plant) in the ground or larger pot?

If so, yes, you can cut the bottom off if you like. If you do, you can use the bottom as plant food by tearing it into pieces and place inside the large pot. I was told I don't need to do it because the roots will break through walls, but that wasn't in my case.