Science cannot provide any such proof given the notion of God is meta-physical and science operates on the physical.
To see its limitations, consider why science is unable to explain why the laws of the universe are as they are: why does heat dissipate, why does fire burn, why do forces follow certain laws... etc
The subject needed to address this question isn't science but philosophy, the discipline that underpins science and gives it its limited methods of empiricism and induction.
Scientific methods have a problem with proof of absence - using observation and empirical approaches, science can prove what is there - however no amount of observations will show something is not there as a future observation may happen. This wiki article elaborates this in more detail: Wiki article about evidence of absence
The other problem is the need to define God to try to prove it and there is no single definition that we can work on. If there was a prediction that "if God exists there must be xxx" we can try to prove that there is no such thing, implying the existence of God is false. Without it the task is hopeless.
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