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I created an Ethereum paper wallet using the files from myetherwallet.com on an airgapped computer. But I don't understand how the wallet can be generated and integrated into the blockchain to be able to receive ETHs without the generator ever establishing a connection to the internet and thus the Ethereum network.

The only solution I see right now is that somehow all possible Ethereum addresses are already available for sending ether to and only the private key is generated to a untouched Ethereum address which I can access then.

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All existing addresses already exist you're right. And in fact when you're "generating" an address you might get one which is already used. But the odds of is happening make it impossible in reality. ( If i'm not wrong there is 10^28 possible addresses )

See here for more information about wallet creation

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When you send to an address, you record that transaction in a blockchain regardless if this address was ever used or not. It only matters if you can send ether from that address. In order to be able to send ether from that address you have to have proper private key and password that this address is derived from. Which is why you choose to send to address that is derived from your private key and password and not any other. You can send ethers to any random address that was never used even if no-one else can ever control it. It's just these ethers will be lost forever.

What matters is how you control your wallet on air gapped computer. You have to use USB stick or flash card or some other way to copy generated transaction to a computer that is online and use myetherwallet or something else to broadcast that transaction. The idea is that this transaction data even if stolen before you broadcast, will not allow anyone else to send anything else from your wallet or change target address.

Does air gap guarantee it's never stolen - I think No. The reason is that you don't know what is inside generated transaction bytes that you copy&paste. Potentially if myetherwallet site is hacked and you downloaded hacked version, it can attach your private key and password to transaction bytes. Since your are encoding it and do not know what is inside, you will gladly copy&paste your transaction to online computer and send it, thus giving control to your wallet to everybody.

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