This is an interesting question. Instant acceleration is mathematically implausible, but I don’t know if there’s a better physical interpretation for what happens to a bouncing photon. I’m guessing this is one of those “less particle, more wave” situations where the instantaneous velocity of the photon is undefined.
According to some random internet sources, reflection is the not-quite-instantaneous process of the photon being absorbed and then emitted by the electrons in the mirror.
As a rule, it’s probably best to avoid “random” internet sources on matters of how light works because there’s so much confidently parroted misinformation out there. For example, this is completely wrong: https://youtu.be/FAivtXJOsiI See here for correct answers to that issue: https://youtu.be/CiHN0ZWE5bk
For how mirrors work see this: https://www.scientificamerican.com/article/what-is-the-physical-proc/ https://youtu.be/rYLzxcU6ROM
There’s a hard rule about quantum physics. It goes: “it’s all fun and games until you’re at the Quantum level, then everything is all fucked up”
According to what we know, electrons don’t “move between” energy states on an electron, they’re just in one one moment and another the next. That’s so disconnected from reality we perceive it still breaks my brain.
