How to immediately turn WS2812 LED strip on after power on?
The WS2812 LEDs are turned on by instruction data shifted through each LED chip. This is explained well in the WS2812 datasheet. There is no simple "pull the data line high for a second and they'll all come on" technique. There is a reset command which is rather easy and that is to hold the data line low for 50 &mu;s and all the LEDs will turn off.

To do what you want would require another microcontroller to send out the light-on commands while the Pi powers up. You would then need to figure out some way of switching to the Pi when the application is running.