I say maybe.
... if for no other reason than when we ask a question and have no information to help us come up with an answer, the default answer is always "maybe": it could be yes or no, but we don't have enough information yet to tell which.
So could God be impossible? The answer is yes... until someone gives a good reason to believe that God is possible.
Does anyone have such a reason?
That which is now has generally always had the potential to be. However, that which is must also be preceded by that which is specifically able to bring it into being. That which is now has "always" been -yet has changed in configuration.
That which is must become a new configuration which makes possible yet other configurations based thereupon.
We see that certain things can not happen at this point without self-aware, intelligent creative activity -and that has essentially always been true, but we don't know exactly how it applies to "everything" because we don't know everything.
Whether we are considering the origin of God or of matter and energy, etc., the answer would be the same. Either it came from nothing or it has "always" been -yet it has become different.
We see that our self-ware creative intelligence is by arrangement of that which exists -so the potential is also part of the basic nature of all that exists.
God would essentially be the whole of everything being aware of itself and becoming increasingly complex in self-configuration. Awareness is basically interaction -so it is possible that it began most simply.
The question then is whether "everything" was necessarily a self-aware creative intelligence (perhaps having developed into such) before our universe and our selves were possible.
Given the nature of our universe and our selves, I would say God is not only possible, but absolutely necessary.
We are made of that which was produced by the Big Bang -and even the singularity capable of self-extracting into the universe specifically was far too complex to have been the very beginning, or most simple arrangement.
The singularity must have been preceded by an arrangement capable of its arrangement -something capable of storing/packaging its potential to become the universe specifically -just as its arrangement was capable of extracting into the universe specifically.
The nature of the universe, etc., is indicative of forethought -but we do not yet know enough about "everything" to determine scientifically that thought must have been applied to cause this specific arrangement.
It also seems logical to me that for God to be all-powerful, God must be the sum of all things, and must have begun with the most simple interactions possible which could become all else by arrangement.
(We, as individuals, begin in a complex arrangement of a small portion of that which exists -and that specific complex arrangement is actually the source of our weaknesses, vulnerabilities and limited ability to interface.)