> you pay this a few times after a deployment or when traffic is increasing and not again.

This is now how lambda works. A lambda instance sticks around for 10s of minutes at most. So you'll have cold starts every day no matter how often you deploy.

If you have very little traffic you might actually have cold starts often as the lifetime of a lambda is determined based on its use.

Unfortunately AWS has always been rather unspecific about this behavior but here's a link to a pluralsight blog https://www.pluralsight.com/resources/blog/cloud/how-long-do...