Nobody takes three months to develop antibodies, the issue was with OLD tests not picking them up, they were there.
The P 24 Antigen shortens the window period further in terms of early detection, if the Antibodies were not high enough to be picked up from 28 days, the antigen would be.
Testing has moved on hugely in recent years, sadly, plenty of the data online and the people peddling it have not.
Best Wishes
James