There isn't one discrete moment — the slide from what we consider "natural philosophy" to "science" is a continuous one. Philosophical notions about atomism informed, for example, the alchemical work of Boyle and the physical work of Newton, even though neither had anything like what we might consider a truly physical understanding of atoms, their action, their structure. John Dalton is typically the one credited for this in the European context, creating a structure in which the atomic hypothesis could (in principle) be used to understand chemistry. But it was still pretty abstract.

By the late 19th and early 20th centuries, you are definitely into the "science" designation of it, in the sense that investigators have a pretty rigorously conceived notion of atoms, their structure (however incomplete), and can interact with them (e.g. the Rutherford-Marsden experiment).

But where did that line get crossed? Was it as late as that, or was it earlier with someone like Dalton? Or was it even earlier, with the Chemical Revolution (Lavousier, Priestly, etc.)? Or earlier, with the alchemists, who, while in a somewhat "magical" tradition of work, were definitely trying to take atomic and elemental theories and make practical results out of them? Creating such a line will depend entirely on what you define as the "realm of science" when applied to atomism, and historians of science tend to reject that there was ever a single, discrete "Scientific Revolution" that suddenly made that jump. (See Shapin's The Scientific Revolution.) But if you are content with fuzzy definitions, one can say, by the late 18th century, many ideas about atomism had, in the minds of the practitioners, transferred out of the realm of philosophy, though they were still pretty vague by late-19th and early-20th century definitions.