Hi,
We recently published some general advice for using the library within FaaS platforms which may be helpful. There will still be a cold start cost to initialise the client, but all FaaS platforms other ways to store global state which removes this cost across executions.
NEST itself has a lot of types to handle all of the possible requests and responses from Elasticsearch. You could drop to the low-level client which does not ship these types and is therefore smaller. However, you will need to handle types to represent the requests and responses.
Cheers,
Steve