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.
What's being rather plausibly suggested, in Moreva's experiment, is a physical apparition of the time dimension. In reality (as compared to what Physics Teacher has correctly described as her "toy model"), such an apparition could only occur (at least in the well-accepted model of time as having a thermodynamic basis) in an overall environment either extremely close to thermal equilibrium (as discussed by Aguirre and Carroll at https://arxiv.org/pdf/1108.0417.pdf), or in one or more relatively small regions causally separated from the remainder of that environment's space: Of those two possibilities, the latter seems much the more probable.
However, although the inflationary cosmological models generally seem to accommodate variations in spatial scale, the only one I've found that implicitly requires such variations is Nikodem J. Poplawski's "cosmology with torsion" (detailed in many papers, written between 2010 and 2020, that are available free on Arvix), which is based on effects of gravitational collapse in the materialization and interactions of known types of subatomic particles, rather than having any basis in any hypothesized field of "inflaton" particles, all of which may remain extremely unlikely to be observable (except perhaps in the last instant of their observer's lifespan), prior to their hypothetical decay into photons, electrons, etc.
Whereas the other inflationary cosmologies are (AFAIK) all based on General Relativity, the torsion-based one is derived from the more recent "Einstein-Cartan Theory" that was developed by Einstein through conversations with Elie Cartan, and is reportedly more complex mathematically, although its compatibility with the CMB data was reported to be complete in a 2015 analysis by Desai. Its basic difference is that it requires all fermions to have spatial extent, which was an assumption often incorporated into pop-sci texts prior to the marvelous practical applications of quantum physics, which have resulted in the current (and perhaps interminable) wait for a theory of quantum gravity.
I'm bringing these facts to the attention of PSE's participants in the hope that some of those familiar with ECT might have the reputation (1,000) adequate to establish an "Einstein-Cartan" tag, which might greatly facilitate comparisons between cosmologies by prospective students.