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?
I'll just leave this here.
Objectivity is a central philosophical concept, related to reality and truth, which has been variously defined by sources. Generally, objectivity means the state or quality of being true even outside of a subject's individual biases, interpretations, feelings, and imaginings.
Might wanna make sure you actually know what you're talking about before attempting correction.
At no point did I make any proclamations about my ability to observe objectively, in fact I stated the exact opposite. How you confused what was so explicitly stated is truly baffling to me.
But if God IS/ARE the laws of physics. Mind = blown.
You keep suggesting he has to operate outside the laws of physics. But if that IS God. Think about it, we are inherently obeying him and bending to his will, because we ALL have to adhere to the LAWs of physics.
Either that or an ancient alien.
Tell me this isn't a serious post? This is nothing but label swapping. We already have a term for the laws of physics, it's...the laws of physics.