Scientists can confirm the existence of atoms using a technique called scanning tunneling microscopy. This is a procedure in which extremely sensitive equipment disturbs a sample at a microscopic level and detects the change in current as electrons of move from atom to atom. Without the existence of atoms, electric current would not exist.
The atom was first postulated by the ancient Greeks through the use of thought experiments. One such experiment argued that there must be a particle of some size that is indivisible. The word "atom" originally derives from the Greek word for "uncuttable." Basic observational data supports this conclusion. For instance, the pre-Socratic philosopher Democritus of Abdera devised a version of atomic theory as early as the fourth century BCE. If physical objects were not composed of atoms, he argued, then movement of objects would not be possible. If there were no atoms and empty space between those atoms, then all matter would be locked in place relative to all other matter. At some scale, there must be an indestructible unit of matter that allows such movement to occur.
This hypothesis was confirmed in the 20th century, when Einstein published a paper supporting the concept of Brownian motion. Furthermore, atomic bombs would not be possible without nuclear fission, a concept that requires the existence of atoms to take place.