|>>|| No. 2805
If you're going to just thin them out then yes use your fingers. If you're going to try to repot them then use something long and thin and scoopy to try and pull out a plug of soil without disturbing the root (there's probably only one per seedling at this point) too much. Not in the same pot. If you've only got the one pot then just thin them out, don't rearrange them as you'll only end up disturbing the others while potentially killing the ones you do move. How many thyme plants do you need, anyway? Even one can grow to quite a substantial size.
The rim of that pot is a bit too high so you've ended up with some really leggy seedlings growing as tall as they can to catch the sun over the edge. Something to consider for next time*.
*If this happens with anything solanaceae (tomatoes, chillies, peppers, some others) it can be a good thing as they'll put out more roots if you pile soil around their exposed stalks.