There is no logical reason to believe that God's existence is not possible. What can be said with certainty is, that was never a state o absolute nothingness ( in a philosophical sense), since otherwise, there would still be absolutely nothing. An eternal universe is not plausible based on scientific and philosophical reasons. The Big bang theory points to the origin and beginning of the universe. The second law of thermodynamics refutes an eternal universe or Cosmos ( Multiverses, Bubble universes, etc. ), and we cannot traverse an infinite period of time in the past.
Intelligence is a known reality and therefore it is entirely legitimate for science to consider it among the possible causal factors in a given phenomenon coming about. Intelligent agency is currently the only causally adequate explanation for the machinery by which the cell translates DNA code having its assembly instructions also coded in the DNA.
Stephen C.Meyer, The return of the God hypothesis, page: 76
It does not follow from the truth of neo-Darwinism or some other materialistic evolutionary theory that a deity could not possibly exist. Even popular proponents of scientific atheism, including Dawkins and Nye, admit that science cannot categorically exclude that possibility.
Dawkins and other contemporary proponents of scientific materialism, of course, claim that scientific evidence provides good reason for affirming that nature is all that exists and for denying evidence of a purposive or designing intelligence behind the universe. Indeed, Dawkins argues that we have a much better reason for believing that God does not exist than we do for believing that God does exist—a belief he characterizes as a “delusion,” because “no evidence for God’s existence has yet appeared.”27 What applies in support of his argument against the existence of God might, however, apply—in light of other evidence—to an argument for the existence of God. Indeed, if it’s possible that one pattern of evidence might provide a reason for affirming naturalism over theism, then it’s also logically possible that a different pattern of evidence might give us better reason to affirm theism over naturalism. To say otherwise would treat naturalism as an untestable axiom or dogma rather than a genuine metaphysical hypothesis that could be true or false depending on the evidence—precisely what Sean Carroll, for instance, is loath to do.