What defines the 'beginning'?
Is it waking from deep sleep, forced or auto light sleep?
Or just power up?
1.8s sounds suspiciously like the time it takes for the ESP8266 to connect to to the WiFi access point when the SSID and password are cached, which is pretty quick!
The lowest power modes that everyone seems to use is Deep Sleep, which triggers a reset to wake, this is required since the RAM turned off in deep sleep and the CPU needs to start from scratch.
This is why i started experimenting with Auto Light Sleep. Since only the CPU gets turned off, and WiFi maintains connectivity.
Another thing that i have found to be super useful is the debugging serial port.
It took me a while to realise what the garbled text that i was getting though the serial port was.
It turned out that the ESP8266 has info that gets put through UART0 at 74880bps.
This includes boot information before the uploaded software is run.
Also, Sorry for the late reply.
I did start a reply but then i realised i had my SSID and WiFi password in the git repository
I must say its not like me to forget about that stuff, but at least that password was one of my more generic public ones.
So to anyone writing source for the ESP, just put your SSID and Password in a header file out of the main repository.