There is. I'll update this post if I remember what it is, but I believe there's a spec and Chrome Canary is supporting it. It uses an HTTP header.
That wouldn't help on the first page load, but it would make the information available on subsequent loads.
I have a feeling there is something else but I have trouble remembering it, too, and I bet I have it bookmarked to study when I have the need to use it.
It's something that literally gets clients to add an HTTP header to specify that bandwidth should be "saved".
Actually, that reminded me of what it was called.. haha, it's https://developers.google.com/web/updates/2016/02/save-data?... .. The header is: Save-Data: on.