we are running pinot on a kubernetes cluster. the pinot server pods takes a lot of time to come up during rolling restart. each pod is taking around 4-5 minutes. Is this time proportional to number of segments in the server? How can I reduce the startup time of the servers?

Have you checked server logs for the segment loading time? Pinot server will reload all the segments before going online.

server container has 7 CPU / 25 GB RAM.

sure, how many segments per sever?