As others have noted, axioms are more akin to a line in the sand—they are either so "obvious" as to be true or constitute such a useful and economic basis for further development that we decide to use them.
Mathematics is more about coordinating human observation and discussion than it is about capital T truth (unless you are a Platonist)
Even if you are a platonist, the conditional nature of axioms is still useful.
Eg look at group theory. It basically says, if you have a set of elements and some operation on this set that satisfies certain criteria (= the axioms of group theory), then you can draw all these conclusions.
I don't think anyone ever argued about whether the axioms of group theory are 'true' in the abstract, because everyone recognises that it depends on your application. Eg they are satisfied for the operations you can do on a Rubik's cube (especially a Platonic ideal of a Rubik's cube), but they aren't true for moves in Sokoban (even a Platonic ideal of Sokoban) nor Tetris.
More famously, look at Euclidean geometry: even setting aside curved spacetime of general relativity, even the ancients knew that Euclidean geometry isn't 'true' on the surface of a globe.