Hi there! I would wait a little longer to transplant, and make sure the grow medium is on the dry end of what's acceptable for the plant. If you transplant too early you will lose a little bit of the benefit of transplanting (growth speed/root structure), and you also risk the soil just falling apart on you and damaging the still young roots. When the time comes I would avoid planting up to the cotyledons as I'm not sure what the benefit of doing so would be, and I generally don't like leaves coming in contact with soil.
I hope that helps, and happy growing! 🌱👍