Now contrast this with the objective - that which is not subject to interpretation. For example, suppose I had filmed the 9/11 terror attacks. No one can argue that two planes did not collide with the WTC because it's right there on video. (ignoring the possibility of doctored videos, which can be detected anyway)
You either don't understand what objectivity is or you're projecting your own definition of it to shape the discussion on your terms.
Everything observed is subject to interpretation. Someone has to observe it and interpret it to be able to communicate it, and senses are not quite "not subjective" to be able to make such a claim that if you don't see it as I do, then you're seeing it wrong. If you did not learn this in your philosophy class; knowledge, the information you use to form any idea, is just memories. In terms of certainty, you don't really "know" anything. You just remember how you experienced it. Convention of knowledge just places your experiences in context in the enviornment you're in, for which it's helpful to understand and predict scenarios within that environment, but it doesn't make that knowledge any less "true" or "false". This applies to every kind of knowledge, including scientific knowledge which is ever changing and evolving.
Saying that you can observe objectively is a sign that you might be an intstrumentalist, which, ironically is a philosophy that is based off empiricism; the philosophy of "experiencing". But either way, even if you're an instrumentalist, you can claim all you want that you can observe objectively, but you can't prove it. Paradox much.
With that out of the way; as of now, no. If conventionalism says there is no observable proof of any god, then it can't be "objectively" verifiable.
But that's very positivist of me, though. I like the more open minded and yet secular answer; given we think the universe is infinite (observably) and the human understanding of quantum mechanics (and for which its mechanical wave function is actually being debated for ontological attribution, lol), I think yes. Everything that can happen has already happened somewhere.
A better question, IMO, is:
Is God's inexistence objectively verifiable?