If one cannot adequately demonstrate that God exists then it follows that neither can one demonstrate that morality must stem from God.
a) It cannot be adequately demonstrated that God exists (many Theists admit this)
b) Therefore morality cannot presently be understood in this manner
Also, if it is found that a God exists it does not automatically follow that morality stems from this being. The question can then be asked: From where does God acquire His own moral convictions? If it is said that morality only stems from the nature of this God then morality itself is nothing more than a set of arbitrary commands. It means that morality still has no basis even within the nature of God himself.
How should morality be understood within the context of human experience then? Morality is understood collectively as an estimation of the drawbacks and benefits of our actions.
Morality is sought within a community but it is also sought on an individual level. Since morality cannot be presently understood as stemming from a God then what is the most likely alternative? Morality stems from humanity. It is an exercise of conscious beings that live in close proximity and intend to find harmony in the context of many differences. Apart from a community morality can be understood as the consideration of how we can benefit others and ourselves in the absence of immediate accountability.
This may not be a very satisfying answer for people that believe, dare I say even expect that morality should be absolute. I’ve even heard many Christians say that if morality does not stem from God then anything goes! It doesn’t reasonably follow that anything goes even within a godless world, however. Humanity as a whole appears to be actively concerned with preventing bad behavior and emulating good behavior regardless of religious truth claims. Preventing bad behavior is done out of a desire to protect our families and our communities. Survival and wellbeing is something our species has labored hard for.
What if it is actually more probable that rather than an uncaused God there is a completely naturalistic explanation on the horizon? What if existence derives from unconscious material processes? I think an Atheistic explanation is potentially less complicated, it assumes a lot less from the onset. To start with a God is to assume that an immensely complicated being acquired all knowledge, power, and even a personality from no source at all. To assume simplicity, in example: unconscious material processes, is to in the very least narrow down the building blocks of a universe that then gradually evolve into something that is more powerful and complex. To presume to know any further into the matter of origins is a failure to be reasonable with the facts that are available to us. The source of our origins may never be known but this does not automatically justify one to assume God in the absence of further objectivity.