This paper shows that 2 photons in a toy universe (isolated box) are seen as static to an outside observer unless interacted with/entangled with. It states that it shows that time emerges from entanglement, I don't know much about physics but wouldn't that imply that without entanglement, time wouldn't exist? But time isn't a physical tangible thing so how can it emerge from something?
An interesting approach.
To answer your question,
time isn't a physical tangible thing so how can it emerge from something?
The idea is to think of time in two ways.
In one sense, "time" is the time that is in the equations of physics. That's the t in the equations of the paper, it's the parameter that describes how the states of all systems in the universe change.
However, actual measurements from within the universe cannot measure "t". All they can do is look at the correlation between the state of one thing - say, the hands of a clock - and the state of another thing - say, the conditions of a chemical reaction. So when we actually measure time, what we're measuring is these correlations.
The paper investigates a toy model, showing that measurements of such correlations from within the system - within the universe - will reveal that things correlate in this way, so that it will appear to things within it that time passes, that clocks measure time and there are processes and states that change in time. At the same time, the overall state of the system does not change in the parametric time t, and if it were possible to make measurements on the whole system from the outside the measurer would see that nothing changes, his measurement results appear all static and the state appears all static.
In this way time "emerges" from the physics: it is the observed time from within the system that emerges, out of how correlations are measured from within.
wouldn't that imply that without entanglement, time wouldn't exist
Yes, if that model captures the way time emerges in the real world - measured time would not exist (but parametric time would!) without entanglement.
That this is actually true is far from certain, even for the writers. They're just offering it as a motivation to explore that idea.
Time is a physical property which cannot exist without Space and vice versa. There is no Time or Space by themselves in the universe. There is only SpaceTime. SpaceTime is curved. Observation is entanglement. Observation is Thought. Thought is a physical property when within the physical universe. Thought is never static and curves with SpaceTime. Though SpaceTime is never static. Yet absent Thought, it appears so, but this is an illusion in the universe; Merely a reflection of the divergence of Space and Time in the linear: Infinity.