A quick look at the documentation link you provided @spacem I see
A cold start is the first time your code has been executed in a while … This process adds significant latency depending on several factors
Remember that functions have a 10 second execution limit so will always run from a cold start. This is not the most effective way to serve a site.
After downloading and building the example static site NestJS offers @duke it doesn’t include an index.html which is the default file for serving on Netlify.