I suppose the answer to this depends a lot on what one understands spirituality to mean. I don't see it as something that was brought in by a religion, but rather something innate to being a human being. Perhaps in some form, in other animals too, but that is beyond my understanding.
I think when one is aware of one's existence, and can comprehend it in the abstract, and is aware of ones own eventual mortality, then spirituality becomes natural.

I am. What does that mean? Will I always be? Is there any purpose and meaning to my existence?

Religions often try to provide answers to these questions, and reassurance to the questioner. But they are a result of the questions and spiritual seeking, not the originators of it.