In a Proof-of-Work protocol, a certain amount of the blockchain's native coin is issued with the minting of a new block as a way to reward miners for their efforts and involvement in the network. As far as I know, though, no coins exist prior to the creation of the genesis block, and after this point, new coins begin to be issued at some rate.
How does this work in a Proof-of-Stake protocol? How does the issuing of new ADA work in Cardano? Was there a certain number of ADA created at the beginning? Or has the 31.9B ADA currently in circulation (out of the 45B max total) all been a product of stake pools forging new blocks?