Einstein's big mistake about entanglement was not taking into account how his own theory of Special Relativity completely modifies the way space, time or simultaneity would be experienced by something traveling at the speed of light for us.
Einstein showed that all moving entities experience some time dilation effects, so time passes differently for each entity depending on its speed.
He also showed that different observers would arrange events in a different order based on their own motion, so every entity has its own idea of which events take place simultaneously, depending on its speed.
But Einstein should have taken these ideas and analyzed what would happen exactly at the speed of light, since this leads directly to the correct explanation for entanglement:
Relativity states that massless quanta at the speed of light (photons, gluons...) do not experience the flow of time, because their proper time is zero.
This means that all the phenomena we picture as propagating at the speed of light would experience no time elapsed, so their journeys would be like instantaneous blinks of existence to them. They would feel leaving and arriving at the same time, with their emission and detection happening at once, regardless of how long or short the spacetime intervals they seem to trace out to us.
So massless quanta can't evolve or change during the intervals we think they propagate at c because, quite literally, they ain't have time for that.
As they don't experience time, they can't experience distance or separation either: The entire span of time we think they traveled at the speed of light gets condensed into a single event for them.
So, in the end, there's true simultaneity taking place in the universe: every subjective time interval we think massless quanta trace at the speed of light happens at once for them. So, for them, emission and detection are simultaneous.
A massless quantum is like a wormhole connecting two spacetime coordinates in no time for itself.
The speed of light is the only speed that would make any entity or phenomenon feel timeless, so light speed is equivalent to teleportation, infinite speed, instantaneity or true simultaneity.
This is the strange point of view all masless quanta experience during the intervals we think they travel at c: A point-instant of existence, where all the events we picture they faced one after another happen to them at once.
This explains how entangled photons (or perturbations of the fields supporting anything in the universe) can show entanglement even when their detections appear separated by large distances or time spans from our reference frame.
For material observers, distances, durations, time intervals and the order of events are relative or subjective, but for each and every massless quantum we think wanders the universe at c, any distance gets compressed to a single point, any interval gets compressed to a single instant, and any sequence of actions gets compressed into a single event.
So it doesn't matter how far apart in opposite directions two entangled photons (or the fields that shape the properties of two entangled particles) appear to us, nor what specific sequence of events they seemed to endure for the time we think they were out there, nor which one got detected before or after the other. To themselves, all the spooky spacetime connections we observe are one and the same indivisible ensemble, where the emission event and both detections form a single and instantaneous action-reaction event with no spacetime qualities.
The correlations observed in EPR experiments come from these "spacetime short-circuits" the massless quanta and field disturbances are able to pull off, but material observers are forced to live inside their subjective reference frames, so they have to create all kinds of convoluted explanations (retrocausality, FTL, superdeterminism, wavefunction collapse...) to try to understand how the correlations can "propagate" through spacetime.
But material observers don't realize their spacetime reference frames are created, precisely, from these instant interactions that comprise all energy and information exchanges that compose anything else physically existing in the universe.
The true nature of entanglement has nothing to do with the subjective spacetime concepts of any material observer, but with the pointlike and timeless existence that all the lightlike interactions that span from a common emission event share.
Take a look to my articles, where I try to explain how light speed is instantaneity in disguise, and how lightlike interactions shape all other phenomena we can observe in the universe:
https://quantumwormholes.medium.com/the-universe-explained-7df2cf8ced90
