Answering the question requires some understanding of the ongoing controversies in the Philosophy of Science. Ontology refers to the existence of objects and effects, and Epistemology refers to human knowledge - how can we come to know about the existence of objects and effects. For unobservable objects and effects, almost by definition, there can ONLY be indirect evidence for their existence (such as Brownian motion for molecules). "Realist" Philosophies of science argue that such indirect evidence is enough for us to deduce (pragmatically) the existence of unobservable objects. "Empiricist" Philosophies say that science does not depend on existence or nonexistence of unobservables. According to these empiricist philosophies, the question of "whether or not atoms exist" can never be settled, and hence it does not matter for science.
The philosophy of science called "Critical Realism" developed by Bhaskar Roy offers substantial clarity on how philosophy matters for the question under consideration, which must be unpacked into two different questions. The ontological question "Do atoms exist (as part of external reality)?" will have the same answer regardless of whether or not there are human beings around to ask this question. The epistemological question is: how can we learn about the existence of atoms (especially since they are unobservable to our five senses)? The answer now depends on our human senses, experiences, logic, theories, etc., and not just on external reality. A crucial distinction is between "certain knowledge" and "uncertain knowledge". If we ask: "Can we be certain that atoms exist?", the answer must be NO. Atoms are a theory about external reality which provide an explanation of a diverse set of phenomena. This provides strong indirect evidence for their existence. Nonetheless, it is always possible that tomorrow a different theory will come along which can explain all of these phenomena. For example, if string theory is true, then what appears to be an atom is really something else, which manifests as an atom at the scales that we can observe. Even more radical theories may be true which dispense with matter altogether.
One school of philosophy holds that knowledge must be certain. If we accept this, then we can never have knowledge that atoms exist. The Pragmatic philosophers, on the other hand, allow for some uncertainty in knowledge. Taking a pragmatic stance, at the moment, existence of atoms seems to be the best hypothesis which allows us to explain a myriad of phenomena, and is coherent with a lot of other theories which are widely accepted - this coherence also provides additional indirect evidence for existence.