That would seem to follow. And it might even entail that only atheists will go to heaven. For an exploration of this possibility, see Only Nontheists Go to Heaven. More likely, however, there just isn't any God. That's a far simpler explanation for why there isn't any evidence of one.
If there is a God, but there is no evidence to be found for his existence except subjective experiences, is it not reasonable to assume that if he does exist, he does not want us to know about it?
The conclusion does not seem reasonable to me.
First, the premise is very unclear, and I will explain what I mean. Second, in the only way I can see that the premise could be considered true, the conclusion does not seem to be reasonably based on it.
AN UNCLEAR PREMISE
First, the premise seems unclear in that it seems to suggest that evidence is the only way to justifiably be convinced of something. But note that rational thought cannot exist without reason behind it. If there is no rational creator god to rationally cause our beliefs, then there is ultimately no possible reason for our beliefs.
Another way of saying this is that the most basic proof of God is that if there weren't one, it would be impossible to prove anything at all. So, if we know anything, then it necessarily follows that God exists. If rational thought is possible, then there is a rational creator God.
I would not personally place a proof like the one I just offered into the category of "evidence". Evidence, in my mind, is never absolutely conclusive. Evidential reasoning always entails some kind of deductive fallacy. This does not mean it isn't useful -- it is. It simply cannot be absolutely certain. Evidence simply cannot go that far.
Instead of calling human rationality "evidence" of God, I would call it "deductive proof" of God. If it is possible to be justifiably certain about anything at all, then God.
So, if there were no "evidence", it wouldn't matter -- we have deductive proof.
This is one way in which the premise is unclear: it seems to suggest that evidence is the only thing that can convince anyone of anything. If this were true, then deductive proof, apparently, cannot convince anyone of anything. But this is surely not the case.
Further, the only kind of "evidence" that can exist for anything at all is "evidence" that is interpreted based on our own personal sensory perception. In other words, evidence by its very nature is always subjective and interpreted according to personal presuppositions.
This is a second way that the premise is unclear. It seems to suggest that evidence can somehow be convincing without being experienced or observed in a subjective manner. But how could this be? What kind of evidence is neither experienced nor observed?
It is through "subjective experience" that a human recognizes that he is standing up. Or sitting down. Or walking, talking, or reading. Such "evidence" does not justify absolute certainty, but it does justify firm conclusions. This kind of evidence is what scientific inquiry is based on -- subjective, experiential evidence... because that's the only kind of evidence there is.
So that is a second way in which the premise is unclear. It makes it sound like evidence can possibly not be subjective. But all evidence is subjective.
THE CONCLUSION DOES NOT FOLLOW
Now on to why the conclusion does not seem to follow from the premise. Given that we have deductive proof as explained above, if the only evidence (non-proof) that we have is subjective experience, it certainly does not follow that God wants His existence to be a mystery: He's proven it!
What's more, even if we didn't have this proof, there are many conclusions humans draw quite reasonably based on subjective personal experiences. Indeed, every single scientific theory is grounded on nothing more than observation -- a subjective personal experience!
So if subjective, experiential evidence were the only kind of evidence God gave us, and as a result we claimed that He wants us to be confused about whether he exists or not, we also ought to be confused about whether germs cause diseases or not, whether gravity attracts masses or not, whether our friends and family exist or not, etc. All of our conclusions about all of these things are based entirely upon subjective, personal, experiential evidence.
I seriously doubt the questioner would say that any of those things should be doubted in the same way that he hastens to suggest that God should be doubted. Yet, if the conclusion followed from the premise, we should doubt all of the above -- every scientific conclusion, every conclusion based on experimentation and observation, ever arrived at!
This is why I've said that the conclusion does not follow from the premise. If it did, the questioner would be throwing out the scientific method and every conclusion it has brought the human race, since every single one of them has come from subjective experiences.
THE QUESTION IS MISGUIDED
In sum, the premise is unclear, even misleading, and the conclusion does not seem to follow from it. Further, we have deductive proof that God exists, such that anyone who denies this fact must also deny all possibility of their own rationality.
However, on the topic of evidence, there is plenty for the Christian faith.
EVIDENCE FOR CHRISTIANITY
Fulfilled prophecies provide powerful evidence that Christ was not just your average human being. Multiple manuscripts, dated earlier than the time of Christ, provide prophecies of the coming Jewish messiah that were fulfilled in Jesus. These include Daniel's prophecy of when the messiah would arrive in Daniel 9:25 (manuscript circa 150BC), Isaiah's prophecy about how he would meet his death in Isaiah 53 (manuscript circa 100BC), and the town in which he would be born in Micah 5:2 (manuscript circa 200BC).
Further, Christianity has a plethora of historical and archaeological evidence to support it. Insofar as it is possible to archaeologically or historically confirm or deny anything the Bible asserts, the claims of scripture have been repeatedly clearly confirmed, and never clearly denied. Examples include the Hittite kingdom, the Israelites' exodus from Egypt, and the reign of Belshazzar.
Christ's coming and existence have been testified to by numerous eyewitnesses, including the authors of three of the gospel narratives, Matthew, Mark and John, not to mention Paul, Peter, James and Jude in their epistles. Multiple witnesses have asserted their observations not only of his life and death, but also of his resurrection! Some of these purported eyewitnesses were so dedicated to their claims to have seen the risen Christ, that they were willing to die before they would deny them. It is reasonable that someone would die for a lie if they sincerely believed it to be true, but it stretches credulity to suggest that people would die for a lie that they knew was a lie, as the apostles would have, if it had really been a lie.
Christ's birth, death and resurrection are the unique doctrinal foundation of Christianity, and it is upon these historical events that the Christian rests his everlasting destiny.
We have all been created by our rational creator God. And each of us has certain obligations that we are morally required to follow -- commands of God. But each of us has, in some way, failed to do what we knew to be right. In Christianity, we call this "sin". The Bible states that all have sinned and fallen short of the glory of God (Romans 3:23), and that the payment we have earned for our sin is death (Romans 6:23). But, Christ was executed in our place, according to prophecy and multiple eyewitness testimonies (1 John 4:10). If we trust His sacrifice on our behalf, we can be forgiven by God for our disobedience and be made right with God forever (Romans 10:9-10).
This is the hope we have in Christ.
Do you think atheists go to hell, why or why not?
Do you "earn your way" to heaven in Islam?
Jesus explicitly says "Many will say to ME (Jesus) LORD LORD, on that day... and I will say to them Depart from here ye that work iniquity" Full context Matthew 7:21-23. What is the Christian's response?
How does a raped woman prove her case in court? Does she have to bring four witnesses?
How is it possible to believe in both evolution and religion?