According to this article, HTTP/2 Server Push is already working for 90% of Internet browsers, with the most notable exception being Safari users. HTTP/2 Server Push makes it possible to bundle CSS/JS/image resources needed by web pages in the initial server response, reducing extra round-trip delays when opening a web page for the first time. https://www.shimmercat.com/en/blog/articles/browsers-with-http2-push/#what-s-http-2-push-and-why-it-is-important-
There seems to be a lot of demand for HTTP/2 in Amazon CloudFront, which could make it easy to deploy in existing services. No ETA from Amazon though. https://forums.aws.amazon.com/thread.jspa?threadID=173140&start=50&tstart=0