The probability of existence ranges between 0 and 1 - essentially it is between impossible and inevitable.
The ways that non-existence can occur is one. The ways that existence can occur are infinite.
Therefore, existence is infinitely more probable than non-existence.
We exist in one of an infinite number of existences. The observations and reasoning about those observations of an apparent beginning and end of "the universe" is merely a limitation in our ability to observe and reason about such things. It may be that what we can observe ("our universe") does have a beginning and end, but that only speaks to whatever this universe is. If existence is absolutely guaranteed to occur some "time" and some "where" in some "form", then the individual instantiations of existence may be transient when considered against the background of an infinite number of instantiations, but it does not imply that there is a creative impulse behind any single occurrence of existence, only that it was inevitable that it happen.
Upon a framework of infinite instantiations of existence, the phenomena we call life is inevitable even if merely by chance due to the infinite number of ways that existence can occur. That we are self-aware and wonder about life's improbability is a coincidence of the configuration of our universe and our emergence in it to observe and reason about it.
Concepts of god and the supernatural are irrelevant in this context - only that which we can observe and reason about, and real things that which we cannot yet observe and reason about, are meaningful.