I think part of the problem is: Science doesn't prove anything. Science, at its core, is simply a method of generating testable hypothesis that explain events, which are valued because of their use in predicting future results.
Let me give an example. Based on observations, science came up with a theory for an orbital period, correlating orbital speed and distance. But it didn't prove this - it's simply the best mechanism for predicting an orbit that science knew at the time. Science could compile evidence that would lend credence to the theory - the more observations that matched the theory, the more likely the theory was sound.
But science could never say, "We know this for a fact." Sure enough, we observed small perturbations in Mercury's orbit around the sun - deviations that the orbital theory couldn't explain. Then we came up with Relativity, which neatly patched those holes. So now we have a predictive theory for an orbit that's better - but we still can't prove that it's absolutely 100% correct. There could by any number of phenomenon that we haven't run into that would tear holes in the theory.
Science never proves anything - the best it can do is say, "Well, this theory is our best explanation for prior events and is the best predictor for future events."
So, let's say there's a God - and not only that, he's completely 100% interactive. Dude just pops in every saturday at NIST headquarters via shining beam of light - even buys coffee for the front desk clerk each week. Science still can't prove him. Because there could always be some unexplained phenomenon that's contributing or even causing our observations.
EDIT: Okay, since there are apparently a number of vocal people insisting that Science can prove things, I figured I should expand this answer to provide some quotes and citations:
"Perhaps most importantly, because new evidence and perspectives can lead us to revise them, scientific ideas can never be absolutely proved."
-- https://undsci.berkeley.edu/article/mathematics - talking about the similarities and differences between Math and Science.
"Well, let me tell you a secret about science; scientists don’t prove anything. What we do is collect evidence that supports or does not support our predictions. Sometimes we do things over and over again, in meaningfully different ways, and we get the same results, and then we call these findings facts. And, when we have lots and lots of replications and variations that all say the same thing, then we talk about theories or laws. Like evolution. Or gravity. But at no point have we proved anything." -- https://blogs.scientificamerican.com/mind-guest-blog/im-a-scientist-and-i-dont-believe-in-facts/
"One of the most common misconceptions concerns the so-called “scientific proofs.” Contrary to popular belief, there is no such thing as a scientific proof. Proofs exist only in mathematics and logic, not in science. Mathematics and logic are both closed, self-contained systems of propositions, whereas science is empirical and deals with nature as it exists." -- https://www.psychologytoday.com/us/blog/the-scientific-fundamentalist/200811/common-misconceptions-about-science-i-scientific-proof
"While the phrase "scientific proof" is often used in the popular media,[13] many scientists have argued that there is really no such thing." -- https://en.wikipedia.org/wiki/Scientific_evidence#Concept_of_scientific_proof - which goes on to quote Karl Popper and Albert Einstein on the topic.
"However, the concept of proof has no place in science. Many people who do not actively practice science do not understand that science is structured so that scientists can never prove anything." -- http://agbiosafety.unl.edu/science.shtml - talking about why it's impossible to prove that biotech crops are safe: because science can't prove it (they can only disprove it by finding a way it's unsafe.)
"Another word that is commonly misused (sadly, sometimes even by scientists, who should know better) is "proof". ... Scientists should be wary of using the term "proof". Science does not "prove" things. Science can and does provide evidence in favor of, or against, a particular idea. In science, proofs are possible only in the highly abstract world of mathematics." -- https://oregonstate.edu/instruction/bb317/scientifictheories.html
Hopefully this helps get the point across, and I tried to stick to purely scientific sources (plus wikipedia, since it has citations to Popper and Einstein). Science comes up with a guess as to how something works, devises a test to determine whether the guess is correct, and then performs the test. If the test falsifies the guess, then the guess isn't correct and was disproven. If the test comes back and matches what the theory would predict, then the test does not prove the theory - it simply is evidence that it might be true.