Whether to treat a system whose behavior you can’t predict in practice as deterministic or indeterministic in principle is a matter of convenience or preference. You can always model it at the level of coarse-graining determined by your own capabilities to observe and intervene on the system, or fine-grain - add hypothetical degrees of freedom to your model - until you have a deterministic model.
The former route is the traditional one taken in quantum mechanics - it’s an empirical fact that the behavior of quantum systems is unpredictable, given our current ability to observe and manipulate them, so most interpretations of quantum mechanics are indeterministic. The latter route is taken by deterministic hidden variable theories of quantum mechanics, such as the de Broglie-Bohm interpretation, where the hypothetical degrees of freedom are simply the particle positions.
A classic example of the ultimate success of the fine-graining approach in physics is the kinetic theory of gases (and more generally the transition from thermodynamics to statistical mechanics), developed well in advance of our ability to experimentally detect or manipulate molecular systems. The first quantitative kinetic theory of gasses was probably Daniel Bernoulli’s Hydrodynamica in 1738 (although interesting qualitative statements can be found in Lucretius’s De Rerum Natura from the 1st century BC). Convincing evidence of the molecular nature of matter came from Einstein’s theory of Brownian motion in 1905 (and its subsequent empirical confirmation by Chaudesaigues in 1907 and Perrin in 1908). In the meantime, as late as 1897, you had respectable physicists like Ernst Mach proclaiming that atoms and molecules were no more than a convenient fiction, forever beyond our ability to observe or manipulate.
Essentially Bernoulli, Maxwell, Boltzmann, and other people who developed the kinetic theory were saying that if gasses were made of lots of little molecules bouncing around according to deterministic Newtonian laws - if those hypothetical (particle position and momentum) degrees of freedom existed - then their large-scale, coarse-grained behavior would be consistent with what is empirically known about their (macroscopic) thermodynamics, including the unpredictable Brownian motion of dust motes in air. Until the 20th century, it was unclear whether empirical confirmation of the kinetic theory was even possible in principle, but in this instance the technique of deterministic fine-graining for describing the unpredictable phenomenon of Brownian motion (as opposed to indeterministic, stochastic techniques, which were also developed) led to the confirmation of the molecular theory of matter.
(brought to you by my patrons)