I don't think that this is possible in pure HTML5. Principally because the stream is not loaded when you see the 'object' in the webpage so the client can't get the desired frame.
However, the best option for you is to save / cache the 'random frame' before loading the page and then use it as the poster of the video. This will allow you to reduce the client work and save the bandwith.
check THIS, which is the first thing that I've found (if you're using PHP and you want a 'quick and dirty' way to get the frame)
Update
Apparently HERE there is a solution with popcorn.js BUT it seems that you can't do it in the way that (I suppose) you need.
This because it would be possible to do this only inside the same domain due to browser security issues.