I listened to Armstrong on Lex Fridman lately. He was originally trying to simply build a bitcoin storage website (a ‘bitbank’). Then he added a buy button and people started using it, but even this did not initially require creating an order book / full exchange. It was a proper pivot by the sound of it.

They actually got to that part pretty early on I think. They had a feature that allowed businesses to accept crypto through them and receive plain old fiat payouts to the bank account. It's still there nowadays, too: https://commerce.coinbase.com/

Edit: it was even earlier than they actually added an exchange – these days it was just a custodial wallet.