You could use a FIFO as input in MPlayer and start playback at the specified time.
I copy paste some minimal code examples I used in a script years ago that were used to skip in videos for scripting reasons.
Create a FIFO:
[ ! -p /tmp/mplayer-fifo ] && mkfifo /tmp/mplayer-fifo
Start MPlayer with e.g.
mplayer myfile.avi -input /tmp/mplayer-fifo
Send the skip command from another script with
echo "seek 10" > /tmp/mplayer-fifo
You can instead use the FIFO to start and pause the video. Use
at to run the play command at a specific time.
If the video is started and then immediately paused and then just waits for the
"play" directive, then all buffering should be avoided.