For example, we may want to explain all the materials we find in nature in terms of atoms. The theorised properties of atoms become the premises that we assume, and we can then prove logically that materials made from these atoms, as we would assume them, would have a number of properties. And then, we could compare the properties so inferred from our premises to the properties we observe the materials found in nature to have. This is of course gross simplification of the actual story but this is the logical backbone.
So, we did that. However, what does that prove? This proves only that if atoms exist as we theorised them, they would nicely explain all our observations of the materials found in nature. But merely finding that the properties of materials predicted because inferred from our hypothetical atoms coincide with the properties we observe the materials to have in nature isn't proof that atoms really exist.as theorised. And as long as we cannot prove these theorised atoms are all there is, we cannot be certain that materials in nature don't have other properties, not yet observed, which could then be a big surprise in store. In effect, we cannot prove the existence of atoms as theorised.
Of course, we went further, explaining atoms in terms of elementary particles, but the situation remains the same from a logical perspective. The difference is between observed properties and unobserved reality. Our models are models of properties because we can observe various properties in nature. Observing properties doesn't prove the reality that causes the properties. Another way to say it is to say that finding n properties doesn't guaranty there is not in fact n +1 properties. And as long as we don't know all the properties there are in nature, whatever our theories, we may end up with a big surprise at absolutely any time. Again, think of dark matter and dark energy.
Still, of course, you can believe rationally that science proves atoms exist, or elementary particles exist. This is all we have, so it is the rational attitude. But rationality is based on what we believe we know, not on what we know.