Hey, Lux! I haven't read the beginning of this thread, so I don't know what gems I'm missing, but I know you are missing one gem, and that is that the people who know God exists and who have a living relationship with Him, are those who have done Him the honor of listening to Him.
The biggest hole in your reasoning (I use the word carefully.) is that you assume people who believe in God have no 'reason' to. But it is precisely because their reason tells them they have encountered Him, that they believe.
Until you are willing to take the risk of having an encounter with God, you will remain deaf and blind to the proofs of His existence, because unbelief darkens the understanding. That's one 'reason' the apostle John wrote that His life was the light of men - because in His presence darkness is removed.
To comment on your thread title, God is both inside and outside of time, but when He is inside time, He retains His eternal qualities as well.