[magawatt (OP)]

Could all the matter created (transformed from energy) in the "Big Bang" be entangled?

[petm1]

The present moment, with a common beginning?

[evan_au]

Quantum entanglement is very fragile - it can be disturbed by interacting with photons and other particles. Most quantum experiments take place near absolute zero, in a dark vacuum.
The Big Bang theory suggests that the universe started very hot and very dense, both of which would have caused rapid "decoherence" and destruction of any initial entanglement.