It's not possible because you as a user can not create a Bitcoin address without going through verification and confirmation of the validity of the address before authentication, so don't be so gullible not to notice the error message of the address if not valid or valid to an already existing wallet.
When your wallet generates an address from a private key, it doesn't check whether the address has been used before or not and there is no way to know whether the address has been generated by someone else before or not.
As already said above, due to having a very large number of bitcoin addresses, it's not possible that the address you generate randomly has been already generated before, but it's not that there's a database of addresses which used by your wallet to know whether the address has been generated before or not.