The theological / creationist method of "prove" is easy:

in contrast to scientific reasoning, where you have to state a theory
that you have to proove, and! that needs to be falsifiable (there needs to be
a way to bring counterarguments, that could disprove the theory)

the theological argumentation is simple:

You start from a view that cant be falsified (there is a god, and god obviousely cant be disproven
- wich scientificly is not a proove, as it is not falsifiable)

Then you argument against the scientific theories, wich are naturally falsifiable.
But the theories are not falsified by correct counterproves, but simply
"disproved" by arguing that parts of the theory are not fully shown/proved.
(since alsmost no theory can be proved by recorded arguments along all its way,
as there is simply not all records available)

Also only theories that contradict in their outcome the theological view are attacked.
If there is enough evidence (like the earth really beeing a sphere), then the next theories are
attacked.

If there are no logical counterarguments, the scientific theories are simply ignored, and
adressed as "godless"