if you go this route, you wait until it 'germinates,' which means the seed has opened and a taproot has emerged. It is important that it never dries out but also isn't sopping wet all the time. that being said, I bet at least half would germinate if you just toss them in a cup of water. That is not a suggestion, just saying that seeds can germinate even in suboptimal environments, but dry = death at this early stage.
1" 2" taproot, then bury it. i don't do this method but that's easy to reference info from a cursory google or duckduckgo search.
i'm not a fan of all these extra steps, exposure to light, and having to manhandle a recently germinated plant. While there's a slight learning curve to depth and how much to tamp down, direct in substrate is a sow it and forget it method with equal or better %-success. Also, there's rarely a need to irrigate the first 4-5 days, so you can leave it unmolested. Get it down and nearly everything sprouts within 3 days.
Just have to get over not seeing it for 3-5 days. Roughly the same amount of growth will have occured, either way. Whether you see it happen or not, same germinatiom success rate.. probably a fraction better since it's less human interaction involved. New taproots are delicate.
Keeping the substrate at 76F-80F (not sure of ceiling) will improve consistency of germination and sprout time. I grow in winter, and a heat mat was worth it. Not necessary in warmer regions or seasons. One with a thermostat+substrate probe, for sure... (best temps for a solid substrate may not be best for how you are germinating them). I only used one the last couple grow cycles, but kicking myself for not getting one before.
Was the water in the cotton very cold? or, in a cold spce in general.
"Seed germination is prevented by a light-sensitive mechanism based on the relative abundance of red and far-red perceived by phytochromes"
--https://www.sciencedirect.com/science/article/abs/pii/S0098847215000933
A seed just needs darkness and moisture..