But, if we define "God" as an entity that created our universe by a deliberate act of will, then my answer is: I don't think we humans could know.
Consider a being, Steve, who says he's the creator of the universe. What test can I trust to tell me that Steve is indeed God? Obviously if Steve fails a test, then he can't be God, but the question is, what human-observable test can Steve pass only if he's the creator of the universe; a test that Steve will definitely fail if he's a very powerful alien of this universe, no matter how powerful?
Chew on that for a moment. (That test you just thought of doesn't work. Steve is a very powerful alien.) Repeat.
Religion qua word-of-God, yes. Religion as an important part of the human experience? No. Religion has inspired the greatest works of art in history. It has been used to justify war and genocide. It brought courage and solace to many in their hour of need. The powerful used it to cause hatred and division in service of their continued power. It has been the foundation of millenary civilizations. It has been the reason for multi-millenial clashes of civilizations. I could go on, but anyone who hasn't got the point by now won't get it at all.
Religion is too complex a topic for simplistic answers. Only the simpleminded think otherwise.
My approach is to treat religion as culture and ideology, where the specifics of a given religion and the acts of its adherents are what matters. Thus, a religion can be separated from belief in a higher being or acceptance of a higher purpose in life, and evaluated as a human construction.
Beyond that, I have the same position towards religion as Winston Churchill: a flying buttress, supporting [the good parts] from the outside.
Sigh! Steve is a really powerful alien who can read minds and obtain all recollections of the dead person from living ones, send a micro-drone to collect a sample of the dead person's DNA, create human clones with preprogrammed brains, and do it fast… shall we say three days, for tradition's sake? The clone will pass for the dead person in all tests devised by the living.
None of these powers makes Steve the creator of the universe.
In fact, Steve need not do anything beyond read and manipulate minds, and humans will not be able to tell with any test. Yes, Descartes figured this out first.
Things that only a creator of the universe could do, such as changing a universal physical constant or a mathematical truth would be hard for humans to measure, what with the universe instantly disintegrating, including us. That's what I mean by not being able to know whether God exists. It might just be Steve. Because, despite being very powerful, Steve is a mischievous alien:
"The arrogance of these barely sentient primates, believing that their paltry 'intelligence' is the pinnacle of achievement in the universe. I'll show them, and mess up their sex lives too." --Steve, circa 4004 BC.
Of course there are other atheists, real atheists, who typically do more interesting things than repeating ignorant internet memes about religion and the religious. On occasion, when asked about God, real atheists' answers are similar to the one above. They bristle at the use of God to justify political positions, even those they agree with, and to exploit the naïve. Most real atheists understand that some religions are an essential part of what built civilization, and respect that. And they understand that religions aren't all the same.
Many real atheists are embarrassed by the shenanigans of the "atheists." And, unlike "atheists," they accept that a religious person can be smart, knowledgeable, and a good individual; indeed, they know many like that.
Gwendolyn, an even more powerful 23-dimensional plasma collective, unimaginable by Steve, restructures the part of the human brain that recognizes rhythm and the associated DNA codons, in all humans, so that Feynman's randomness will appear as a high art form to all generations of humans hence. Thus Gwendolyn unwittingly creates late 20th-Century Earth music.
ZXKW-99, a dark energy sentience of varying dimensionality, with capabilities beyond what Gwendolyn can conceive, goes to Earth's Permian, finds the ancestor of all mammals and encodes 'Feynman bongo-playing sucks' in the genes for myelin, using an obscure 24th-Century Earth quaternary code. By accident, that makes the ion pumps in mammal neurons immune to diclorodiphenyltricloroethane.
God, outside the universe, observes the ongoing tomfoolery and considers changing the value of $\pi$ to reset the universe. Floods are so passé.
-- -- -- --
Bonus round - geeks only
What about a message inside a physical or mathematical constant? Say a message around the twenty-trillionth digit of $\pi$, encoded as a sequence of $p \times q$ ones and fives, where $p$ and $q$ are two large prime numbers, indicating that the ones and fives are to be arranged in a rectangle of sides $p$ and $q$. That message can only come from the creator of the universe.
So, Steve arrives on Earth, points the mathematicians towards the constant, the computers do their magic, and lo and behold, the $p \times q$ rectangle has a picture of Steve in it. That's proof that Steve is God, right?
Nope. At best, it proves is that Steve found the message and was able to change his appearance to look like it.
It also suggests that the creation of the universe was an act of will by an intelligent entity, and hints that there may be more messages, possibly using other numerical bases. Except that we're making a few unstated assumptions.
Ok, so it is possible for a creator of the universe to send us a message which will lead to the construction of a technology that would validate communication with that creator… if we could be sure that the numerical expansion, the interpretation of the message, and the construction of the apparatus were not being influenced by malfeasant aliens. Three big ifs.
The problem is, how could we be sure that our numerical analysis wasn't being hacked by Steve? That our interpretation wasn't being primed and guided by Steve? That our apparatus wasn't simply a Steve-detector, designed by Steve to create The Church of Steve?
Note that Steve doesn't really change $\pi$, he inserts that message in the computer, not the number. Only the creator of the universe can change $\pi$, but many human teenagers know how to crack into computers and change their code. And some of these human teenagers have read Carl Sagan and understand the use of prime numbers for creating rectangles and passing messages. So Steve recruits them with promises of Jolt Cola lakes and Pop-Tarts mountains.
Alas, the Church Of Steve is brought down when a Caltech student notices that "MIT Rulz!" is secretly embedded in every page of the Cosmic Encyclopedia used to build the God-detector.
God smiles and congratulates itself for creating nerds.