As one of my secondary school teachers said long ago, the first thing to ask is, what is your frame of reference?
In other words, how do you define exist?
Existence can be one of those words that just circles around and get you nowhere. That which exists, is. If something possesses being, it exists.
So what is being?
Dictionary.com doesn't help, because it defines "exist" as "to have actual being; be" and "be" as "to exist." Which sounds circular to me.
But the frame of reference is the key. That which exists, in my view, relative to our anthropomorphic perspective, is that which, yes, occupies, space and time.
But is there an afterlife? Is there a God? If so, do either exist in that they occupy space and time? No, certainly. Either lies (if it exists) in a spiritual realm.
Let us say, for arguments sake, that God exists and s/he is spiritual. God is. God possesses being. But God exists quite outside of the realm discernible with the five senses with which humankind are blessed.
So the frame of reference for space and time is human sense. Beyond that which we can sense, we cannot know with any degree of certainty what exists. But we can conceive of the possibility of existence of something, like God, souls, heaven, with our mind.
The brain is something tangible; the mind is spiritual. Indeed, I am among those who believe that the spiritual aspect of our nature is represented by the mind. Our minds can take the leap of faith (a necessary thing) to believe in the existence of something invisible, spiritual, occupying no space and time, but its quite difficult because, as humans, all we have to work with is what we see, hear, smell, taste and feel.
Certainly its mind-boggling, but our puny little minds can take a crack at it and imagine that something beyond our ability to comprehend can nonetheless really exist.
