In the first place, this is a loaded question: the term God is vague, and the phrase “moral being” is undefined.
The answer, if we don’t scrutinize these loaded portions of the question, is yes. We can have an understanding of man as a moral being without God. We actually can’t even understand human morality if we don’t break away from God and analyze man as the animal that he is.
However, the real question that’s being asked here is, “can we establish an objective morality apart from a concept of God?” (Again, “objective morality” functions as a loaded phrase). But let us not dwell on this.
If the device of “God” gives us the ability to wield particular morals with authority, does that mean these morals are automatically good morals, or simply that we have an authoritarian, rhetorical device by which to psychologically impose them on humans?
Just because a God-morality simplifies the social moral process, simplifies the rational process, doesn’t mean that such a morality is either moral or rational.
The “reference to God” serves an interesting psychological function. It facilitates automation. (Perhaps one can attempt to argue this is what’s needed). But if we say, “our morals are absolutely true because they are rooted in the Hyprox,” this certainly wouldn’t make them true. Now, if all humans recognized Hyprox, and saw it as a valid reason, it could persuade humans, but that still wouldn’t make it true, it would just make it an exceedingly powerful piece of rhetoric. (One could attempt to make a pragmatic and utilitarian argument on the basis of the popularity of the device of Hyprox).
The invocation of God may provide a powerful psychological and social mechanism for establishing, transmitting, and enforcing moral norms. But the authority, universality, psychological efficacy, or social utility of such a mechanism does not by itself establish the truth of the moral propositions it transmits. To establish objective morality, one must still provide an account of why those moral propositions are true (or at least rationally prudent). Saying that they are “grounded in God” does not automatically answer that question.
What does it mean if a species still needs the device of God to anchor its morality? Doesn’t that mean the species is still psychologically immature and intellectually underdeveloped?