If you want to measure, just set a pin high when you're done setting up everything and measure the time between power on and that pin going high. Easiest with a 2 (or more) channel scope.
Or just use a arbitrary time based on trail and error...
One thing you can do, is include code to send a client status response message in response to a poll from the master. Then when you initialize the master, have it poll the client for a ready status.
Then you don't have to measure the startup time or estimate a safety margin.