CMV: Objective morality is not justified

I enter many theological debates where it's often posited that objective morality exists, objective morality couldn't exist with God, therefore God exists. I think that argument fails with the first premise and I'm interested in exploring it more.

My stance is that if objective moral facts exist, there should be some reliable method to identify and justify them. There is no discovered method that can reliably do this. Reason, culture, intuition, religion, and other human factors all give inconsistent moral judgements. When a claim has no reliable way to be identified or confirmed, there's reason to doubt it exists. If a belief can be sufficiently explained by human factors, and has no way to to be verified as objectively true, the default position is that it is a subjective phenomenon. Therefore, we have good reason to conclude morality is subjective until objective moral facts can be shown to be true.

I wholeheartedly think the only way to escape this is to establish morality as an objective social behavior in animals as an evolved trait. However, I think what it would really come down to is a set of certain evolved traits like empathy or altruism. These don't establish any objective moral facts, more so just an engrained guide that has been successful in social flourishing.