One approach is to use a reiterative method, with a deliberate inclusion of the steps of
1) searching to know your assumptions
2) working out the results of those assumptions
3) comparing with reality.
When working with assumptions (axioms) there is no known direct way of testing them. You need to test the results.
To see how hard this can be, look at geometry. For a very long time, Euclidean non-curved geometry was thought to be the only possible one. Then the two non-Euclidean ones were devised by modification of the parallel lines axiom. One gives a curved geometry for closed situations. The other gives a curved geometry for open situations. IIRC, the current assumption is that the open type best fits an expanding universe.
I wonder how many other things we "know for sure" aren't that certain
