The soul (spirit) of man is part of man, it became part of man somewhere during the process of evolution. The soul is a sign of God which is a mystery no mind can ever unravel.
The Spirit of God does not exist on earth as part of humans. God, who is Spirit and not flesh, always remains in His own high place in the spiritual world (heaven), seated upon His Throne of Glory. That is how I understand the Baha'i Writings.
If, as I believe, God is unreachable, remaining in His own high place, how then can God also be omnipresent?
I believe that God, who is Spirit, is out of reach, but God's knowledge and power is universally present.
I like this definition of omnipresence:
In Western theism, omnipresence is roughly described as the ability to be "present everywhere at the same time", referring to an unbounded or universal presence. Omnipresence means minimally that
there is no place to which God's knowledge and power do not extend.
Omnipresence - Wikipedia