Earlier quoted context omitted.
Sure, Google could do but there's more than enough problems vs reward to make it unattractive: - When you fast forward VHS tapes you still see the adverts. When you time seek a digital video file you don't. - It's harder to do targeted advertising (since you no longer know if the downloader is also the viewer) - Adverts baked into a video file can't be changed out later for newer adverts after the user has downloaded…
What do you mean by "technical issues"? Google already has a streaming video player supporting multiple bitrates and formats. They could just do whatever youtube-dl does to pack it into a file or even more optimally, grab it from their video database directly should there be something like that.
But I grant it's technically possible to do with a single MPEG file, just not trivial. You would need to prepend the advertisement to the video bitstream (re-encoded with same parameters such as width, height, FPS, intra picture interval) and then do the same for audio, while ensuring the video/audio synchronization is kept intact (MPEG edit lists are not well-supported by players, such as by ffmpeg), while preferably not re-encoding the actual video. A bit more complicated to do the insertion in the middle of the file.
It's possible to do, but I don't think it's something that any off-the-shelf tools actually do.