My understanding is that EFS is exposed as an NFS share. I haven't used it personally, but NFS mounting is generally fast, nearly instant. What does "load in the entire datastore" mean?
Many servers start up, load a ton of data from storage into RAM, and then happily serve that data for a long time. The latency of the server when starting up before it can service its first request is entirely based on the throughput of the data load.
Often these servers will load 128+GB of data into RAM (crazy, huh?) and even if you have 1GB/sec it's still two minutes for the server to start up.