I would not worry about thinning thyme seedlings. When I sow thyme seeds for growing, I liberally sprinkle seeds over the cell pack or pot and just let them be. You will end up with a nice, thick stand of thyme when you are ready to transplant or plant out. I grow 100s of plants each year for our MG plant sale and this method has not failed me for thyme. It makes for a nice full plant. A 6" pots sounds OK for where your plants are at this stage.
Once your thyme has a few sets of true leaves, you can transplant it into a larger container if you wish. Don't know where you're located, so not sure about your plant out date. You may wish to edit your profile to give us an idea of your growing zone so we can provide more specific advice.