IMO, only those that reject Christ are not saved.
And as Jesus is part of God, and as one most certainly CAN reject what they DO know of God without knowing the full details about the Jesus part of Him, then they most certainly CAN reject God without knowing the Gospel. Interesting that in Romans, Paul speaks of what God HAS made clear to heathens that came before - and very interesting that He doesn't mention a whit about their lack of knowledge of Jesus or that this knowledge would have saved them. In FACT, it very much suggests that they have ALREADY rejected God in what He has ALREADY revealed to them - and that is enough for their condemnation. Now, will there punishment be less severe, etc? Yes, perhaps. But that does not mean they will be saved.
And to reject something means that you have known it and decided it is not for you.
No, God does not decide whether one will reject or accept Him. He leaves that opportunity and responsibility to them, although He will no doubt lure, steer and encourage those who are willing to listen and obey at least what He shows them. The more He shows and they positively respond, the more He will provide - and He will provide all necessary to the one whom truly wants to know more.
You can't reject something you have no knowledge of.
True. BUT, God has made ALL aware of His existence and basic provision - and people can and do reject THOSE! Also, while we know God will be most merciful, just and loving, we don't know or see all that He does. I would very much agree that those mentally impaired, children before certain understandings, babies, etc, that they are saved upon death - or at least provided and understanding that they can they fairly decide for themselves what their response will be to Jesus.
You can't reject something if you do not have the mental capacity to understand what it is OR what it means to reject it.
That's unScriptural, that is, the part about not understanding what it means to reject God. The mentally ill, children too immature to understand their sin and responsibility - those are another issue! Also, post-Christ's resurrection, we have no Scriptural basis for seeing one come to Salvation independent of them FIRST hearing the Gospel (Romans 10:17). Remember, it is GOD Whom places all in time, place, history, etc - and He does so according to HIS eternal plans. So, no jungle, no remote place, no time in history, is too vast, obscure or a hurdle for Him to reach people. We must trust that. He MIGHT reach people who have not heard the Gospel in some different ways, but BEFORE death. We just can't know for certain.
People who reject or don't believe because they have never had a chance to believe, for no fault of THEIR OWN, will be saved because God's grace is given NOT because it was earned or because it was merited, but because God LOVES Us and gives it freely to all those He chooses to. Why would he choose to deny it to those that He KNOWS don't know any better ?
Again, many DO know better - or at least enough. What is implied here is that many people have an INFORMATION problem, and yet most in America, surrounded by churches preaching the Gospel, the Bible online and explained prolifically online, etc, etc - and yet most here, absolutely saturated with the Gospel available, nonetheless choose to reject God. What MOST have is not an information problem, but a HEART and MIND problem - that is, they want to "serve the Creature," they want to ONLY obey that little god they see in the mirror every morning. And if NOT being familar with the Gospel would be akin to a "get out of Hell free card," then we should cancel most missions work ASAP! We should just keep the heathen safe by making sure they remain ignorant of the Gospel. Why do you think the Great Commission is even important, IF ignorance of Jesus would be a positive thing? That makes absolutely NO sense!
Read a bit of Romans 1 and 2. See what the heathen DO know and what they CAN reject, without extensive knowledge.
One other thing: To AVOID God, to not search for Him, to pretend His existence is unknowable, to buy into lies denying Him, to adopt false, heathen religions, (and, espescially) to deny Jesus is God or His crucifixion or Resurrection - these ARE all forms of rejecting Him!
Bottom line is, we don't know exactly how God deals with everyone, everywhere, everytime - but we DO know what His Word says, let's not go beyond it in our understandings. Let's not ASSUME that ignorance will lead to bliss. That sounds very much like universalism, to me!