I think the way "believe in nothing" is applied to science is in terms of the null hypothesis. One must compare an experimental finding to chance--and by rejecting chance as an explanation one has supported a claim.
If one can't reject chance, one goes back to the drawing board.
A scientific claim is never fully supported--but is bolstered by replications and related findings which also cannot be satisfactorily explained by chance.
The intent is to reject chance, and when we can't, we try to design a better experiment.
I think philosophically one wants to (maybe even must) reject the belief in nothing--even if the alternative proof is a bit insufficient--just like we must reject the null hypothesis in science. Belief in experience of some kind may be a good start.
Those who would challenge any alternative cannot accept the "nothing" hypothesis any more than scientists with the null hypothesis. IMO, most real atheists reject spiritual hypotheses in favor of materialist alternatives, not philosophical "nothing"--and they must prove them against "nothing"--just like spiritualists.