After the first photons of light are produced, which process is responsible for amplification of the light?

Stimulated emission is the fundamental process behind laser amplification. When a photon interacts with an excited atom, it can trigger the atom to emit a second photon of the same frequency and phase, creating an amplification effect. Blackbody radiation and Planck's radiation describe thermal emission processes, not coherent amplification. Einstein oscillation is not a standard physics term in this context.