Firstly make sure you boot straight into X. For details on this, please see this question: Auto-start X-windows / gdm on the standard Debian buildAuto-start X-windows / gdm on the standard Debian build
Then edit your ~/.xinitrc
file. It needs to contain the command that starts your media player:
vim ~/.xinitrc
omxplayer -p -o hdmi /home/oliver/awesome.mp4
This will make the video begin as soon as X does.