It could be possible that a regular family doctor test for low testosterone levels?

Depends: The most important thing is to get it done in the morning, from a reliable lab. Even large labs like quest or labcorp have problems doing reliable testosterone levels at the regional sites. The "trick" I use is to order a "bioavailable testosterone". That way the test is done in a specialized hormone lab that does it reliably. Any low level needs to be repeated before starting medication