I'm not certain you understand the nature of a Bitcoin address. It's a 160 bit hash of a ECDSA public/private keypair. They "exist" in the entirety of that gigantic space, but as it's utterly infeasible to generate even a fraction of that space, a non-broken wallet implementation will generate a unique key pair and 160 bit address every time you create a new one.
In theory, yes, multiple people could independently end up with the same public/private keypair and therefore the same Bitcoin address, able to spend each others funds - but in practice, given the keyspaces involved, that simply means there are some utterly broken random number generators in place.
And that's been attacked in the past. Ages ago, "Brainwallets" were a (poorly thought out) thing - generate a phrase, hash it, use that to derive an ECDSA keypair, and, hey, wallet based on a phrase you memorize. Except, humans are horrible at generating random phrases, so various people went around hashing various phrases, checking the addresses, and helping themselves to any funds found (and if I recall properly, enough to have been well worth the effort, especially if they held some).
But trying to brute force private keys on the blockchain (which is more or less what you're describing) is entirely infeasible against a well implemented wallet and random number generator.