The proposed god must be defined
Evidence for a vague higher power may not support a personal, morally perfect or tradition-specific god.
Evidence should be more likely if the claim is true
An observation supports a divine claim when it is substantially more expected under that claim than under ordinary alternatives.
Private experience has limits
Visions, sensed presences and answered prayers may be meaningful, but similar experiences support contradictory religions and can have psychological explanations.
Public and repeatable evidence would be stronger
Clear predictions, independently verifiable events or reliable effects unavailable through ordinary causes would provide stronger support.
Ambiguous natural events are weak evidence
Beauty, complexity and existence itself may inspire theological arguments, but they require comparison with naturalistic explanations.
Evidence should identify the correct god
An unexplained event does not automatically establish the deity, scripture or doctrine preferred by the observer.
The absence of expected evidence also matters
Claims that a god regularly intervenes, answers prayers or reveals truth create expectations that may be tested.
Evidence notes
Strong evidence would be independently verifiable, resistant to ordinary explanations, specific to the proposed deity, consistent across observers and capable of generating successful predictions.
Ethical questions
Does the evidence support this specific god or merely something unexplained?
What natural or psychological alternatives remain?
What evidence would count against the claim?
Conclusion
Evidence for a god would need to distinguish divine agency from coincidence, natural causes and human interpretation. Unexplained events alone do not establish a particular religious conclusion.