Influences cannot travel faster than the speed of light, but particles can be entangled at separate ends of the universe because both sentences are true at the same time, since they are caused by one and the same thing: What constitutes phenomena propagating at the speed of light to us, material observers, means instantaneity for the massless quanta involved.
And it’s kind of tragic that Einstein, who created the EPR paradox to prove that Quantum Mechanics was incomplete (and ended defining entanglement), already had the solution before his eyes. It was hidden in his own theory of Special Relativity, which completely modifies the way space, time or simultaneity would be experienced by something that appears traveling at the speed of light to us.
Einstein showed that there's a limit for the effects of any interaction, and that would be the speed of light. But he didn't fully grasp the consequences that travelling closer and closer to the speed of light has for how time flows, and crucially, what would happen exactly at the speed of light.
Special Relativity states that if we could travel as close to the speed of light as we wanted, we could traverse the whole universe in any unit of time (proper time) we wanted, just by adjusting our speed closer to that of light. Time will tick slower by the time dilation effects of our speed, and if we could reach the speed of light exactly, then time will stop ticking altogether. We would experience going nowhere in no time, leaving and arriving at the same time. Emission and detection (and anything in between) would be the same instant blink of existence for us.
This is exactly what the massless quanta (photons, gluons...) and field disturbances that appear to propagate at the speed of light to us are able to pull off. What material observers experience as different spacetime intervals is always "condensed" into a single blink of existence for the massless quanta involved. Any distance, duration or sequence of events we think they covered, lasted or endured gets compressed to a single point and instant of simultaneous, timeless existence for them.
So it’s not a matter of either having interaction effects propagating at the speed of light, or spacetime coordinates being entangled instantly, it's both at the same time, just experienced from different perspectives.
The moment we introduce space and time to describe how the universe works, we're choosing a particular frame of reference that is only valid for a specific set of material entities. But the objective reality of any massless entity is what it experiences for itself: that "no time elapses", regardless of what any material observer could have to say about that.
So the true nature of any photon or gluon is the instant bridge it represents through spacetime, not the subjective time interval of any observer. We should stop thinking that massless quanta are entities, processes or field disturbances propagating at the speed of light through spacetime. They are more like instant connections between different spacetime coordinates that comply with the light speed ratio.
Photons and gluons don't experience our spacetime dimensions. They don't know what “here”, “there”, "before" or "after" even mean, so they are the whole emission-flight-detection process, somehow.
Then, any photon or gluon represents a kind of entanglement between emitter and absorber, and the speed of light is the incredibly distorted way in which their instantaneity can be understood from our subjective reference frames.
This explains how entangled photons can show weird correlations, even when their detections appear to be separated by large distances and time spans from our reference frame: It doesn't matter how far apart in opposite directions two entangled photons appear to us, nor what specific sequence of events they seemed to endure for the interval we think they where "flying" out there, nor which one appears to be detected before or after the other because, to themselves, all the spooky spacetime connections we observe are one and the same indivisible ensemble, where the common emission event and all related detections (no matter how scattered through spacetime) form a single instantaneous action-reaction event with no spacetime qualities, as long as the intervals we observe for them keep them related by the speed of light. Each carrier we detect still feels linked to the entanglement event wherever/whenever it gets detected, by virtue of the speed of light.
But if the speed of light is key for entanglement, then, how is it possible for some material particles to show entanglement at speeds other than c?
This is only natural once we understand that any piece of matter is just a structure of fields, or a network of fundamental interactions, and that massless quanta and field perturbations are not little carriers that propagate through spacetime at the speed of light, but more like wormholes or "short circuits" that instantly connect different spacetime coordinates, always complying with the light speed ratio.
So the light-like interactions that unfold each time form a network of instant relations that interconnect spacetime from past to present, stitching reality each time. All the massless carriers we picture as travelling through the universe at the speed of light are, at the same time, the instantaneous entangled connections that create the spacetime structure itself, the information exchanges that hold up reality and make it self-referential and self-consistent with all its past history automatically. Entanglement is, then, the fundamental principle that drives the universe.
When we prepare a Bell experiment (be it with massless or massive particles), we are not creating the right conditions for entanglement to develop, we are creating the right conditions for entanglement to show up.
It is not that massive particles can display entangled properties under some specific conditions, it is that entanglement underlies every physical property, structure, process or phenomenon existing in the universe.
Much in the same way, any energy or information exchange we usually picture as a process can now be seen as an instant action/reaction event enforcing a conservation law, so entanglement is not a consequence of conservation laws, it is entanglement which supports and enforces those conservation laws.
This dual perspective of light speed as instantaneity does not only explain entanglement or the EPR paradox, but it also shows that the wave function collapse and the measurement problem are non-issues (since every massless quanta is a collapsed wave function the moment it emerges into reality), and explains a lot of the other puzzling behaviours and interpretations that plague Quantum Mechanics without the need to call for extra dimensions, parallel worlds, retrocausality, superdeterminism, faster than light communication, wave function collapse or any other convoluted spacetime mechanism we conceive to solve a spacetime problem massless quanta don't even experience.
I explain how light speed implies instantaneity here:
and how the instant (but light-like) interactions that unfold each time shape everything that exists in the universe here:
https://quantumwormholes.medium.com/the-universe-explained-7df2cf8ced90
