The whole universe is the “god particle”, let’s call it “universal potential, the totality of all.”
As for entanglement, entanglement breaks down through heat and interaction. Entanglement must be insulated and maintained (in mass) or it decays by environmental interference.
I’m fairly sure that entanglement is the synchronization of a hyperdimensional vibration, of which there are more unique vibrations than there are particles in the universe, so theoretically yet not practically, one might change the vibration like a radio dial and run across the entangled synchronization with the randomized vibrations of all other particles. You simply would never know if it were entangled with a random mote of dust drifting in the cosmic void, or otherwise.
This said, I also believe not being synchronized gives each particle a unique scope of identity. Thus it allows our minds to be subjectively our own (by default), and yes I propose that our minds entangle and may entangle.
Be glad no such correlation as you suggest exist, for fools always believe their wisdom is the extent of universality. There is always something more even great minds have not yet considered, and one may never know how existence may be manipulated for whose own interests.