If BTC was sent to an address before it was generated, could a newly created account have BTC from the start?

I was daydreaming about a person 50 years from now that is gonna generate a new wallet and freak out when they realize they won the fucking jackpot!

How likely is this to happen? Has it ever happened yet?

Satoshi said “Lost coins only make everyone else's coins worth slightly more. Think of it as a donation to everyone.” Does that mean that when you accidentally sent bitcoin to a non-existent address you just donated to the future bitcoin billionaires lottery?