Thank you very much, yes, you correctly understood my question. I would like to speculate on this topic:
Those. when Satoshi began to mine, and every 2-5 minutes a new block appeared, and he received a reward for the proof of his work - she came on! a randomly generated wallet !, this wallet was generated by the customer himself, the "first miner" btc, right?
and these keys (private key) from this purse were automatically recorded somewhere? tell me more pls.
Bitcoin addresses (ie. public / private key pairs) are unrelated to the PoW mining process.
You
first need a valid Bitcoin address, then you can receive transactions on it -- including block rewards. That is, Satoshi's wallet existed
prior to them mining the first block. Otherwise there wouldn't have been a Bitcoin address onto which to receive the coinbase transaction containing the block reward.
(Also note that even when Satoshi began to mine the targetted block interval was 10 minutes, like it is today. Supposedly Satoshi's first block following the genesis block took hours, if not days, to mine, but I'm not sure if that story is just apocryphal since I can't recall the source)