The issue seems to be, bitcoins don't exist anywhere, as such. Before or after they're mined. What exists is the value on the network, as expressed by the code. And yes, insofar as their value is accounted for in the code, that value exists before mining. We can think of mining almost like when authorized shares become outstanding shares when they are issued. They exist ahead of time, but they are only considered to have any value (in fiat terms, and in the case of stock, voting rights as well) once they are issued. Just like the issuance of authorized shares into outstanding shares dilutes market value, so too does the mining of bitcoin dilute the market value of outstanding bitcoin (even if we often just express the market cap based on the 21 million figure out of what amounts to sloppy accounting).
Discussion
Analogy is good but I don’t like the idea that the value exists before issuance. The bitcoins exist, but their value is yet to be decided because they haven’t touched a market. But their quantity has already been fixed.
That's a valid concern, and it's not a perfect analogy. Authorized stock is not a hard limit in the way not yet mined bitcoin is. Perhaps it's better to think of Bitcoin not yet mined as existing, but belonging to an entity who has published its schedule of "spending them" on the labor and resources used by the mining network. That entity being the network itself.