I’m using the Npgsql driver in a .NET application to connect to a CockroachDB instance. I set Minimum Pool Size=100 in the connection string, expecting the pool to pre-open 100 connections at application startup.

What's your expectation here exactly with regards to "application startup"? Opening a connection is a heavy, asynchronous operation, when exactly are you expecting that to occur?

Because there's no natural, implicit place for such a startup operation, as @UtlaMincykun wrote you can simply do a quick for loop and open the connections yourself wherever is suitable for you.