The hypothetical 200ms is for cold starts. That means when the docker container that runs behind the lambda first starts up.

When a lambda is invocated, that docker container isn’t immediately destroyed. It’s kept around for reuse.

So there isn’t a realistic scenario where you would get a million cold starts in a month.

Some companies who actually depend on actions like this should consider fronting some cash to keep this project going.

If you have cold starts on all of your millions of requests, something is very wrong with your code.