Absent irrefutable evidence, I would say, "not." "Almost completely irrefutable" is the same as "irrefutable" to the same extent "almost completely alive" is the same as "alive" (i.e. not at all.) A somewhat ironic difference between proof and evidence is that negative forms of the latter, but not the former, are possible.

The root problem is that existence of a deity is a metaphysical question, but many materialists pretend that is somehow not a metaphysical position and therefore not subject to metaphysical rules. That is no more valid than a biologist insisting cells are unaffected by gravity, or a geologist claiming rocks do not oxidize.

Absolute proof of anything is difficult to impossible to obtain, in law, philosophy, science or anywhere. The best we can do in nearly every case is a very high degree of evidence (and I contend negative evidence against a deity is far from irrefutable; quite the opposite, IMHO.) Yet the difficulty of obtaining absolute proof does not grant the ability to claim rational certainty absent proof, only preclude absolute certainty in nearly all cases.

We cannot rationally say, "Well, OK, disproving a deity would be proving a negative and therefore impossible—but there is still no deity!" Appending "OK, there might possibly be a deity, but there definitely is not" makes the first statement less, not more, rational.