We had huge problems with Java and Lambda start up times. I would strongly recommend python/nodejs or maybe Go. For whatever reason .Net core was still slower but not Java holy crap slow.

It seems to be. It can be "cold" when the lambda hasn't run at all in a while and the first instance starts, or "cold" when due to increase in load, or for whatever reason that you're not supposed to know or care about, instances are running but it runs on a new instance.