There's no such thing as instantenously "pushing" on a particle. E.g. electrons can be accelerated by electromagnetic fields. If the field changes, the electron

There's no such thing as instantenously "pushing" on a particle. E.g. electrons can be accelerated by electromagnetic fields. If the field changes, the electron feels a force and is accelerated according to a = F/m (handwaving away relativity). When you macroscopically push against a rigid body, what happens at the particle level is your constituent atoms' electrons (and protons) interact with each other through the electromagnetic field.