Don't thin out yet. What you have there is the "seed leaves" or cotyledons, that store nutrient from the parent to get the new plant off to a good start. At this stage the stem is far too fragile, and if you try to thin out you will snap a lot of stems and kill the seedling. Wait until they have all developed try leaves, and the true leaves have reached about an inch across. Don't worry about rate of growth - it'll slow down enormously as the food reserves in the cotyledons runs out.
To thin out, this is how I'd tackle it: first slide a flat blade under the soil at the edge of the tray, and get an idea of how bound up with roots it is. If the soil is still free and crumbly, hold the most convenient seedling by its true leaves (not its stem), while gently teasing it out of the soil. Reach for pot while still holding seedling, put a thin layer of soil in the bottom, hold the seedling over the pot with its roots in the pot and the top of the roots just below the level of the rim. Scatter soil gently over the roots into the pot, shaking gently now and again so it settles, until the roots are covered, then firm down the soil with your thumbs, add a little bit more if there's still room (don't come quite to the top of the pot to allow for watering). Sometimes it's helpful to plant a bit lower in the pot, so the soil comes further up the stem and gives a bit of support. If the compost seems dry, water it gently. And in any case check in 24 hours and water gently if the top of the compost is dry. Try to keep the compost moist but not wet.
If the soil is a tangled mass of roots, find a bit where the planting is less dense, hold the soil in both hands, and simultaneously shake and gently pull your hands apart until you now have two pieces, each with some seedlings in. Repeat until you have a piece of soil with only one seedling, pot it up as above. And carry on.