Our co-evolution with viruses has been going on way way way longer than 800 yrs and will continue. They can evolve a lot faster than we can. New variants emerge. Fortunately, a product of that co-evolution is an adaptive immune system whose function is to respond to new infectious agents. It works great in healthy people but does require exposure so the adaptive immune system can read, respond and remember the new agent. But its hallmark is specificity; that exposure is unlikely to be nearly as effective as inducing adaptive immunity against related coronviruses. Same reason there is a new flu shot each year.
If you are suggesting that there is somehow a CoV-2 related coronavirus that pre-exists the pandemic, persistantly infects humans, as is being revealed as a CoV-2 false positive in the PCR assay there are a number of negative controls to rule that out. In fact, the precision of PCR, which comes in the primer design, is one of its strengths. Its sensitivity, however, can be both a strength and weakness.
If by time stamp in the infected you mean how rapidly after infection viral genomes can be detected by PCR or otherwise that has been pretty well worked out, most cleanly in cultured cells but also in real infections.
