Your bottleneck would not be the building of the test (https://www.thermofisher.com/us/en/home/brands/thermo-scient...), but the FDA approval. The CDC was able to get emergency use authorization from the FDA in 1 day for its test, but you are not the CDC.
Ah, I thought you were trying to solve the broader bottleneck of testing which would require approval. But as a hobby just for fun, I suppose you could do anything you want...not sure how useful it would be (would you trust your result? Would health agencies take your result as evidence?)