I am a bit confused what kind of test Ben is referring to here. If this is about smear tests, RKI says that it may be possible to show evidence for an infection about 2-3 days before symptoms begin. However, medical professionals warn that it’s not trivial to take the smear test and that therefore laypeople conclusions may lead to wrong negatives. If it’s about blood antibody tests, there may be false positives because antibodies may those formed against other corona virus infections.
According to Harvard //www.health.harvard.edu/diseases-and-conditions/if-youve-been-exposed-to-the-coronavirus
We also don’t yet know at what point during the course of illness a test becomes positive… you will get a false negative test result [on a swab test] 100% of the time on the day you are exposed to the virus. (There are so few viral particles in your nose or saliva so soon after infection that the test cannot detect them.)… About 40% of the time if you are tested four days after exposure to the virus
So this sounds like, with a smear or swab or saliva test, you’d want to wait up to 4 days after potential exposure, and a false negative remains possible.
I believe I’ve seen elsewhere that the saliva test is comparable to a swab in accuracy, but is more foolproof (because you don’t have to take a sample from your throat).