I believe God’s spirit is eternal. I was AG for 18 years and was told that God’s spirit has no beginning and no end, but human spirits have a beginning but no end.
I was told that but never given sound scripture to support it. I eventually abandoned that belief. If we do not accept Christ, I do not believe we have an eternal spirit. In fact, I question whether we have one at all if we are not saved.
We reason on time as flowing, as a linear thing. Time is a volume. Eternal existence is existence not on a linear scale but a volume, always present, never past and never future, always in the present, eternal in existence. Eternity is the volume of Time.
Put in a more modern framework, the 'information' of being is not lost, it resides in the volume of Time. Even Stephen Hawking is beginning to get it, since he has backed off on his earlier notion of a black hole collapsing infinitely, with nothing escaping. That's why I write that a black hole is a fair though not perfect analogy.
Genesis 1:26