In the standard courses of classical mechanics inertial reference frame is defined as a frame with respect to which every free material point, i.e. not interacting with other bodies or fields, moves uniformly.
Then the first Newton law says that inertial frames do exist.
I realize that the notion of inertial frame is an idealization. As far as I understand, the meaning of the first Newton law is that for a given problem one can find a frame which can be considered as inertial with sufficient accuracy.
To make the first Newton's law useful, one should be able to apply it in concrete situations. If I understand correctly, for Newton himself one of the main examples of interest was the planetary motion, he tried to explain Kepler's laws (based on Tycho Brahe's measurements). As far as I understand Kepler (or Brahe?) used the Copernicus frame to describe the planetary motion, i.e. the frame where the Sun is at the origin.
Usually in textbooks the Copernicus frame is claimed to be inertial for planetary motion. Why?? How one can check the definition? I have no idea how to find sufficiently many free bodies in this frame and verify that they move uniformly. The gravity forces of all planets acting on such bodies should be negligible. How it could be done practically?