Growing medium for Thymus Serpyllum

I am a hobbyist who is trying to use a lot of Thymus serpyllum as a ground cover and as a plant between flagstones. I like it because it produces lovely little red flowers. I hope I have the correct plant.
I am trying to grow Thymus serpyllum using your seed and also seed from other sources.
I have experienced total failure. Here is what I am trying to do.
In early August - this year and previous years - I have simply moistened soil in the area where I wish to grow the Thymus serpyllum , then I sow the seed as close to random as I can, water in, with a fine nozzle spray and then I try to keep the area moist but not sggy. Nothing comes up.
This year, in mid July, I filled 120 little 2"(5cm) pots with "compost" soil, settled the soil well by gentle shaking and sowed the seed lightly into each of the pots.
The seeds germinated rather well and rapidly. Then, over a couple of days, the small green paired cotyledons disappeared. I don't have a single pot that has plants that moved to the second leaf stage.
What am I doing wrong?
By the way I used the same technique for French sorrel and I have a bumper crop of seedling that are now into the second leaf stage.
Should I simply use milled peat moss as a starter soil and then feed lightly with a balanced fertilizer?
I may be forced to use your plug trays - although I would like to save on the expense. Since I would like to plant several 100 plants.
Can you help please?

I wonder whether the plant you admire is actually creeping thyme. It comes in reddish and white flowering cultivars while the T. serpyllum (now called T. pulegioides) has more lavender flowers. Both are pretty, but the creeping thyme has redder flowers and is lower growing.
Your first attempt failed, because without loosening the soil and doing something to allow the germinating seeds to never dry out, they WILL dry out and even once is death. You should loosen the soil, work in some compost or DAMP peat moss and then sow the seed, rake lightly, water with a mist and cover with evergreen bows or other shading that will not smother the seedlings. Keep constantly moist- a hard thing to do in July!! You will have better luck in the cooler month and best luck in spring, when the seedlings have all summer to grow big and strong for the winter.
When you sowed in the pots I did not notice you saying anything about tamping the soil down a bit or watering it to consolidate it a bit.The air holes may have been so big, that the roots dried out. Also, using compost could be a mixed blessing unless you pasteurize the moistened soil at 400 degrees Fahrenheit for one hour in the oven before use. The compost heap gets all sorts of infected discoloured plant parts thrown into it and unless it is composted very correctly with the resultant high temperature, it will still contain plenty of pathogens. Not good news for tender seedlings.
If you use peat moss as your seeding medium measure its pH first. There are both acid and alkaline peat mosses and you will have to adjust the pH to be between 6 to 7 to have thymes thrive.