First commercial AIDS test was available 1985, but they found AIDS patients because their rare diseases and weakened immune system. There were tests to find certain antibodies which were presumed to be from AIDS virus. So there was a lot of speculation and several published reports about AIDS and possible virus behind it on summer 1983.
It is also speculated that this virus was generated in the US military lab to reduce world population or it was created by chance when hepatitis B vaccine was created in early 1970's and then tested on homosexuals.

I may be wrong but I think it was the commercial HIV test that was available from 1985. Blood could be tested for AIDS from 1983 onwards. However the test of course wouldn't have been instant. But I remember there was a major blood screening campaign (in the UK anyway) in 1983 so AIDS could be identified from blood then.

This part of the show was way off the mark. The first AIDS test was available in 1985
Duty Now For The Future

for me that moment in the car when the AIDS issue is revealed was one of the most terrifying moments in the series I lost too many friends to that dreadful disease I remember the 80s too well.
it was very very well done

Yes, it was, but it took atleast 6 weeks to confirm the diagnosis.