The speed of germination of Celosia (and any other seed) is largely dependent upon the temperature of the germination medium. The use of heat mats or heating cables greatly speeds up the process, reducing the chance of rot. Once the seed has germinated, the heat source can be turned off.

With heat, celosia can be expected to sprout in about 10 days, give or take. If you leave the seed uncovered, even faster, though you'll need to take care that the seeds never dry out.

I'd start your celosia 4 to 6 weeks before your average first frost. Be sure to provide plenty of light after germination, as these full-sun seedlings will become leggy.

I don't remember which of the hybrids I grew a couple of years ago, but they starting blooming their little heads off within 5 weeks, maybe even sooner. Cool air temperatures, I believe, speeds up the bud formation.