The genesis transaction creates the initial supply. All mined coins should then be coming from the genesis transaction address.
Every block mined creates new XMR in its coinbase transaction (also known as the miner transaction). The first block (the genesis block) is no exception, it created 17.59 XMR in its coinbase tx, and as this was the first ever Monero tx, it's also known as the genesis tx. Thus, every XMR in existence has come from these coinbase transactions.
Note, this is the same as with Bitcoin, the coins don't exist until they are mined.
What address does the coinbase transaction come from?
So if you're following above, they don't "come from" some address. They are created as outputs spendable by the miner of the block.
From reading the monero source code, it seems that the COIN_SUPPLY variable is defined as (unint64_t)-1, which is the max unsigned 64 bit int value. Why is it done this way instead of defining the actual max supply as COIN_SUPPLY?
It's MONEY_SUPPLY (not COIN_SUPPLY) defined as -1, and it's done this way because Monero has a tail emission – coins will continuously be created as a reward for mining blocks.