Can they test all babies born in hospitals at birth?

Certain things: It has become a standard every infant gets tested for syphilis, metabolic diseases (newborn screening, used to be called "pku" test), and hearing defect.

Yes!: The newborn screening is universal for all babies to test for various disorders that may be present at birth. Most of the problems screened for can be very serious if not addressed early in life.

Odd wording: Whether or not a newborn gets a specific test or any tests at all depends somewhat on the parents.Usually they sign a permit for normal testing . Universal screening for a variety of problems has been going on for decades in every state, some states testing for more things than others. There is no "universal" test that picks up every possible problem, but there are many.