It is possible to reduce start up times considerably if the Wifi channel and router mac address are used when configuring the stored connect parameters. This reduces start up time to 1 second or less depending on the router response.
The fast connect is particularly useful in deep sleep applications to be more responsive when waking and minimising active time in battery applications.
I have modified a version of the standard tzapu WiFi manger to support this. Normal operation is unchanged but if a call is made to setFastConnectMode(true) before calling WiFiManager autoconnect then when the app is configured it will use this fast method.
I have made a pull request for this change but the code is available in my fork at
https://github.com/roberttidey/WiFiManager
The support is in the development branch.