Deriving the Bitcoin address from the raw block script
Surely the address must exist first before the raw block can allocate the mined coins to it?


No. The network has no concept of addresses. When you send money, you're actually sending funds to a public key or public key hash. The Bitcoin address format you're familiar with is just a way of representing public key hashes in a human-readable way.

This is especially true of generation transactions, which typically send money directly to a public key. Bitcoin-Qt normally doesn't calculate or display the address in such cases, though it's still possible to calculate it.

The "coinbase" doesn't contain the address or public key. That's just mostly-arbitrary data. It contains the block height, extraNonce, etc. The address is in "scriptPubKey". In the genesis block's generation transaction, the scriptPubKey is:

04678afdb0fe5548271967f1a67130b7105cd6a828e03909a67962e0ea1f61deb649f6bc3f4cef38c4f35504e51ec112de5c384df7ba0b8d578a4c702b6bf11d5f OP_CHECKSIG


This is a direct-to-public-key transaction, not a normal address transaction. 04678... is the uncompressed ECDSA public key. Follow the instructions on that wiki page to get the address, 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa. But again, this transaction doesn't contain this address, or even its base58-decoded (binary) equivalent. The address is just a way of representing the public key.