Not a professional so some of my terminology may be wrong, but here is how I understand it: after your immune system fights off a virus it often develops 'antibodies' to fight off the same virus if it should encounter it again. We can detect these antibodies via a blood test and thereby get an idea of whether you've had that particular virus before.
Yes, but confidence of detecting antigens becomes more difficult for some infections than others. And some viruses stay in your body like CMV. In the case of COVID-19, the virus does not remain, but the antigens do. The question is can the test detect them long after recovery. I'd like to know too for my own curiosity and to see if this means I am immune to it for this strain, this season.
I strongly suspect I caught it from a friend that had travelled all over Europe and back the previous weekend and we were in close contact.
Unfortunately no way to rule out if I indeed had it or not. Would be super interested when an antibody test comes out to see though.