If all particles which have once been entangled remain connected, then if we accept the idea of a Big Bang (the long term viability of which as a final explanation of the creation of the universe is far from clear) then all particles in the universe must have been once entangled. They were in the same infinite mass from which everything comes.
I don’t know what ideas of physics I might be violating or not knowing here, but I thought I would put the idea out into space.