Is everything quantum entangled?
By far the most particles in the visible universe aren't quantum entangled. That's obvious from observation, since if all electron spins e.g. would be entangled, all electrons would flip their spin at the same time, and we couldn't observe varying statistics of electron spins in a sample, resulting in varying degrees of magnetism, e.g. by applying gradually changing exterior magnetic fields.

A second example: All (bosonic) atoms of spin 0 would form a Bose-Einstein condensate not just near absolute zero, since they would be in the same quantum state, hence in the lowest.

The "single source" isn't a single quantum state. In the early phase of the big bang temperatures were very high, allowing for a huge amount of possible quantum states within a small volume. Without warranty you may think of the initial state of the universe as a superposition of all possible quantum states, the wave functions of which collapse relative to an observer, regarding the observer as a particular quantum state.

That way we get to the many world interpretation of quantum theory and a universal wave function. See also a proposed Hartle-Hawking state as a pre-Planck epoch of the universe.