I know this question may seem obscure, but I'm trying to get a deeper meaning to what allows us to "push" things at a macroscopic level. And since all forces can be broken down or derived from the 4 fundamental forces (as I have read), I'm assuming its the EM force, (repulsion of electrons in atoms?). Please correct me if I am wrong! Cheers!
Rather than "applied force," the correct term is "normal force." "Applied" is not a type of force in a classification scheme.
The normal force requires both electromagnetic interactions and the Pauli exclusion principle. The question of how normal forces arise microscopically is essentially the same as the question of why bulk matter is stable. The definitive paper on this is Lieb, Rev Mod Phys 48 (1976) 553.