We spawn a Postgres instance on the fly if it isn't already up in just a few hundred milliseconds. Cold start times are always something we try to improve.

(Neon engineer)

A process? Or like a container with Postgres in it?

It is a VM which is hosted in a Kubernetes pod.

We just run everything on a small cheap Threadripper with a mere 1/2TB RAM, it just sits in the co-founder's basement.