First of all, the idea of fundamental particles (also called elementary particles) relates to the question of the nature of the universe: what the universe is made of. This question has been asked since as early as 6 BC. Those asking this question then and since are thinkers such as Democritus, Dignāga, Ibn al-Haytham, Dalton and Rutherford.
Fundamental particles are defined as those particles that have no substructure, that are not made up of smaller particles. It was once believed that the protons and neutrons were structureless but it is now known they are made up of quarks. Though information has changed over time, the idea of the fundamental particle began with history's earliest thinkers.