Is the assumption of the existence of entities in a mathematical model required for science to work?

Yes and no. This is typical question working in probability interval <0, 1> so it has no meaning to vote about it.

The "existence of entities" can be quite contrived concept even for quite trivial things like the gravity, magnetic field and/or atoms. On the other hand, the solely abstract models tend to remain, well - untestable and abstract. From physical perspective it's always better to use observable and tangible concepts for to keep theories falsifiable and testable. One abstract postulate in otherwise physical theory still isn't a big problem, but multiple ones already are. See also:

Hartry H. Field: Science without Numbers. Is the assumption of the existence of entities in a mathematical model required for science to work?

Yes and no. This is typical question working in probability interval <0, 1> so it has no meaning to vote about it.

The "existence of entities" can be quite contrived concept even for quite trivial things like the gravity, magnetic field and/or atoms. On the other hand, the solely abstract models tend to remain, well - untestable and abstract. From physical perspective it's always better to use observable and tangible concepts for to keep theories falsifiable and testable. One abstract postulate in otherwise physical theory still isn't a big problem, but multiple ones already are. See also:

Hartry H. Field: Science without Numbers. Hartry Field argues that we can explain the utility of mathematics without assuming it true. He already demonstrated that Newtonian theory could be formulated in the way that no abstract entities is needed (assuming spacetime points are real then).