You're assuming that "no God" is the null hypothesis. Is there a good, rational reason for this?

In general, it's not rational to posit that anything exists without evidence. Out of the set of all things that could be posited, most do not exist.

"Evidence" need not be direct observation. If you have a model which has shown good predictive power, which predicts a phenomenon you haven't observed yet, the model provides evidence for that phenomenon. But in general, people here would agree that if there isn't any evidence for a proposition, it probably isn't true.

ETA: see also Absence of evidence is evidence of absence.