The genesis block contains a phrase from a newspaper article "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks" in the coinbase transaction, which proves that the genesis block could not have been created before Jan 3 2009. This proves that there was no pre-mining before that date, assuring fairness in distribution.

If there was no genesis block, individual miners would need some way to come to consensus about which news paper article to use and whether they meet the criteria of it being printed on that date and this would be extremely impractical.

But otherwise, I believe it would be possible to have a blockchain without a genesis block.

The genesis block contains a phrase from a newspaper article "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks" in the coinbase transaction, which proves that the genesis block could not have been created before Jan 3 2009. This proves that there was no pre-mining before that date, assuring fairness in distribution.

If there was no genesis block, individual miners would need some way to come to consensus about which news paper article to use and whether they meet the criteria of it being printed on that date and this would be extremely impractical.

But otherwise, I believe it would be possible to have a blockchain without a genesis block. There is nothing that is particularly special about the very first block except for what I mentioned above.