Do you ever have dreams? Hopefully the answer is yes or else this is going to fall a little short.
You dream about other folks. They do things say things. Are you consciously controlling anything they say or do? I'm assuming you've experienced this.
They seem completely autonomous, not under your personal control. So we know in a dream state at least the subconscious mind is capable of creating the experience of interacting with autonomous beings.
Did you know the color pink doesn't actually exist. However your subconscious mind creates the experience of seeing pink. So the subconscious mind is capable of causing you to see something that isn't there.
Your conscious self is dealing with only 2 to 3% of your mind. What going on in the other 97%, you're completely unaware of. The reality you perceive is all filtered by you subconscious mind. Consciously, you get a fraction of the sensory input that the central nervous system is capable of.
All of this should be pretty easy for you to Google and verify, that plus your own experiences should be enough to validate what I'm saying.
Now I'm not saying this is proof there is no God. I'm just saying the subconscious mind is quite capable of providing a spiritual experience.