It seems it is unlikely but not imposible to create a wallet and find some bitcoin.
An address is basically a number (plus some other stuff), so all addresses "exist". Addresses are not "activated". You can send bitcoins to any valid address, but only someone with its private key can spend those bitcoins.
The number 0 has this address - 1111111111111111111114oLvT2. Over 300 BTC have been sent to it (mostly by accident). But until someone discovers its private key, those bitcoins can never be spent. It is extremely unlikely that its private key will ever be found. The inability to find the private key for an address is a foundation of Bitcoin's security.
Also, a quick clarification of terms:
- Address: Bitcoins are sent to an address. An address is derived from its public key. It is not a public key or a wallet.
- Private Key: Used to control the bitcoins at an address. A private key is not a password or a seed.
- Public Key: A public key is used in a transaction and is rarely used directly by a person. A public key is derived from its private key. It is not an address.
- Wallet: A wallet contains and manages private keys and their associated addresses. A wallet is not an address. A wallet typically uses a seed phrase to generate all of its private keys.
- Seed/Recovery Phrase: Used by a wallet to generate private keys and their associated addresses. A seed phrase is not a passphrase or a private key. A seed phrase is also known as a recovery phrase because all of a wallet's private keys and associated addresses are derived from its seed phrase.
- Passphrase/password: A passphrase is used to encrypt a wallet, private key, or seed. A passphrase is not a private key or a seed phrase. However, sometimes a wallet will add an extra word to the seed phrase to be used as a passphrase.
Here are sets of terms that are frequently confused with each other:
- Public key <==> Address
- Address <==> Wallet
- Private key <==> Seed Phrase <==> Passphrase
Terms that should be avoided because they are ambiguous or probably being used incorrectly:
- Wallet address: A wallet typically does not have a single address associated with it.
- Public address: Use of this term typically indicates a confusion between the terms "address" and "public key". All addresses are public.
- Public Key: Typically this term is mistakenly used in place of "address".