A lot of great advice from veterans here already. I had similar issues, i.e. seedlings not growing at all for weeks. Repotted in a high quality mix and, well, lesson learned. Instant growth.
The only thing I might add, and it's not entirely necessary, is the pot/cup looks kinda big for the plant in the first pic. I've had better experience potting up more gradually, first to 2" pots, then 4" pots, etc. Nothing fancy, just whatever works. The tiny plants just don't transpire much, especially if it's cooler, so it can take awhile for the soil to dry (especially not good for peppers). Not necessary if stay vigilant on proper watering, but I think it can be more fool proof when you're just getting your bearings. Just my .02.
Also, I've burned plants with LED's too. Quantum boards are a different ball game, but the mfgr should have height/setting advice for different stages of growth. For 1000 watt board and seedling stage, they recommend 24" distance and 60% brightness. Of course YMMV.