Smallest Possible Video File in H.264 Format
A one frame H264 stream would have to consist of an intra-coded frame, so there is a size floor in effect.

This ffmpeg command produces a 1.7 kiB file

ffmpeg -f lavfi -i color=blue:s=1280x720 -vframes 1 out.mp4


You can save ~200 bytes by lowering the resolution.