Newton's Second Law
While we may not be able to "see" a force, we can feel how hard we have to push on a box to move it across the floor. We can readily suppose that two bricks exert twice as much force on a scale as one brick. We can even measure this by noticing that the deflection of a spring supporting two bricks is twice that of a spring supporting one brick.
So physical forces are measurable. Further, they are measurable without referencing Newton's second law. Or differential equations.
People had been measuring mass with balance scales for thousands of years. One need not belabor that point.
Measuring acceleration can obviously be done with rulers and clocks. So Newton's second law can be seen as a physical statement about measurable quantities.
In modern physics the correctness of Newton's second law is taken for granted and we actually define the standard unit of force in terms of the standard units for mass, distance and time. The reason we do this has more to do with what quantities we can measure precisely than with what quantities are "physical" or "fundamental" (whatever those terms might mean).
Having done this it might seem that Newton's second law is a matter of definition rather than a matter of experimental fact.
This is very similar to the way we take the constancy of the speed of light for granted and define the standard unit of length in terms of the standard unit for time. That's because we can measure length using atomic clocks and interferometry better than we can measure the distance between two scratches on a rod, not because time is more physical or fundamental than distance.
Having done this, it might seem that the speed of light is a defined constant rather than an experimentally determined value.
