In Spain you go to your healthcare doctor and ask, and they will usually grant you the blood test, but it depends on them. I never had any issues though.
Yep, expect for this weird COVID-19 year, were it's advised to no overload the health system, usually you would only need to see your GP and tell him/her "it's been a while since last check up" or "I'm feeling weird/tired/not sleeping well" and usually they would begin by a basic blood test.