I'm sure you've heard it before: God can't make his existence known to us because then we could not have faith. It makes sense at face value. But, there are many interesting factors involved that are often left unexplored. Most of them undermine this argument when left unaccounted for. Others are just of casual interest.
The claim made most often is that God making his existence known clearly to us takes away our free will to decide whether or not He exists (though the linked webpage asserts that we still have free will even with proof, because we are biased for or against Him anyway.) So, God can't make his existence too clear, otherwise we would all have faith in him by default, and obliged to worship him, rather than doing so without knowing about his existence. The strange thing, though, is that God supposedly takes satisfaction out of being worshipped with faith that he exists, rather than being worshipped with faith that he is good and worthy of worship (this also being presumed in the latter form of worship). That seems a bit arbitrary, and it remains unclear why He would expect people to make both of those leaps of faith, when one is big enough (given what we know).
Now, the most obvious problem is that God needs to make his existence known in at least some respect, or make us aware of him in some vague manner, because if he did not, we would have no grounds at all to even imagine such a thing, much less believe it to be true. A "God" (the Christian God and whatever hypothetical others that might be relevant to a discussion of "faith") that gives absolutely no signs is a God that will never be thought of in the slightest. If we were to come to the conclusion that he exists, there would be no exerted pressure to stick with that particular imagined construct, and no reason, among all things the human mind could conceive of in order to explain the things that God is really supposed to explain, why we would come up with the right answer. But, this much doesn't matter, because that form of God, not interacting with us in anyway (and not interfering with our supposed free wills) just isn't consistent with the Biblical God.
Divine revelations, miracles, and existence itself are all touted about as proof of God's existence (with the latter two being claimed to have happened clearly and undeniably in, well, Biblical times). "Divine revelations" and "prophecy" today, however, are mostly dismissed as insanity (save by those who really want to believe them). They are deemed to be hallucinations and dreams, as the linked article tells us. Of course, considering the incredibly subjective nature of these events, and how they seem to be entirely internal experiences, it is hard to conceive of a time when such things weren't dismissed outside of circumstances in which people wanted to believe them, because their delusions confirmed the worldview of the listeners. It becomes hard to imagine how men distinguished between those who were "divinely guided" and those who were "stark raving mad" aside from such preconceptions. And it is even harder to imagine, if this confusion is God's desire to keep himself hidden, why He spoke to several people simultaneously, according to some Old Testament stories. It seems that he appeared to several of them individually and subjectively, but he spoke to Noah and his sons together (thus making it a little harder for them to have the free will to doubt his existence), and he actually appeared to Moses and 70 other people in order to tell Moses to go to Mount Sinai for the more personal, possibly hallucinatory encounter. He seems to be good at keeping us in the dark now, though. Guess it took Him a while to catch on.
Then there are miracles, of which "God revealing himself" might count as a subset (or perhaps miracles are subset of God revealing himself...who knows?). Miracles have seemed to have gotten staler over time. That said, it would be possible to dismiss even the Biblical "miracles", in the form of cities being wiped off the face of the Earth by magic, women turning into salt, people being spontaneously forced to speak different languages, parting oceans, raining frogs, and all those marvelous events associated with the End times. Those are not necessarily indicative of a God existing, and does not force belief, but it is enough to make you question the way that the world works. We, unfortunately, do not seem to see much of that kind of thing anymore. Nothing that is clear and unexplainable violation of everything we know, and witnessed by many. We do not even have the privilege of seeing how we would deal with explaining these things because they do not happen. Miracles today involve a single flower standing in the middle of scorched forest, missing a taxicab that wound up in a pileup, or White Jesus showing up on a grapefruit somewhere. No rain of fire, or cities decimated by clearly supernatural forces (in lieu of, say, hurricanes). It's another case of God being a non-interventionist only outside of holy books. But, in those books, there was one alleged source of miracles that would have been far harder to deny: Jesus. He supposedly churned out miracles like he was some sort of miracle factory. The guy walked on water, turned water to wine, casted out demons, multiplied food products, revived the dead, cured blindness and disease by touch, and claimed that God is real, and he was Him. If he actually did those things, it would be rather hard to doubt that he was telling the truth if you were paying attention to him. And that also doesn't look good for free will. A God that manifests itself and showed off his tricks 2,000 years ago doesn't exactly sound like the kind of God that wants us to rely on almost zero evidence, for fear of disrupting our ability to choose. But, unfortunately for us, all we get is old accounts of how those miracles happened by biased observers written decades after the fact. At least he appreciates our "free will"!
And, then there is the muddy matter of asserting that existence itself is proof of God's existence. This is a common argument independent of this one, and it is clear that if existence is all that we had to go by in order to decide whether or not a God exists, God is really expecting too much with too little guidance. Mostly because, unless one conceives of God a priori (tampering with free will again), one would never come to the conclusion that God is responsible for existence, because, without knowledge of that God to begin with, it is just an arbitrary guess. It is the equivalent of me saying that I associate Gremlins with star formation. Stars exist, and therefore Gremlins exist. I might get lucky, and Gremlins might be responsible, and my acknowledging that might appease them. But, more likely than not, it is just something incredibly random that I have come up with to explain what I see before me by speculating about something that might possibly be responsible, but is beyond disproof due to an intentionally slippery definition of Gremlin (anywhere from goblins, to spiritual craftsmen, to a metaphor for gravitational and nuclear forces). Existence is definitely a highly subjective proof of God's existence and doesn't guarantee belief. Mostly because it isn't proof at all.