Light isn’t accelerating. Cars and rockets are. A photon’s momentum and kinetic energy are part of the photon, and are imparted to it instantly as the photon is created in some interaction between particles. Ultimately, it “pushed off” of the particle that emitted it; that particle gets a slight recoil in the other direction (usually a pretty small one, since the momentum of a photon is typically small compared to the momentum of typical particles).
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