Each node in a Bitcoin network has no physical address in the mempool or Bitcoin blockchain, only scripts. A Bitcoin address represents just a number, and the number that the address represents is a simple way of talking about transferring control over value to us humans.
 Simply put, it's a human-friendly way to show senders and receivers what addresses are in their wallets, and if I send someone my address, I'm basically instructing the sender's wallet to generate new output with a script derived from that address.
My wallet can see the sender and receiver addresses, but it shows exactly my wallet address. Within the wider Bitcoin network, I can display the addresses used by my transactions by converting transaction output scripts into an address representation of how to represent that information as a number via standard rules.
Within my wallet software, bitcoin addresses exist as soon as my wallet private keys are selected. So any address will exist as long as the number position exists.