As clearly stated, most users of ffmpeg are unaware of them using it. Even them knowing about a vulnerability in ffmpeg, they wouldn't know they are affected.
Really, the burden is on those shipping products that depend on ffmpeg: they are the ones who have to fix the security issues for their customers. If Google is one of those companies, they should provide the fix in the given time.
But how are those companies supposed to know they need to do anything unless someone finds and publicly reports the issue in the first place? Surely we're not advocating for a world where every vendor downstream of the ffmpeg project independently discovers and patches security vulnerabilities without ever reporting the issues upstream right?
If they both funded vulnerability scanning and vulnerability fixing (if they don't want to do it in-house, they can sponsor the upstream team), which is to me the obvious "how", I am not sure why you believe there is only one way to do it.
It's about accountability! Who really gets to do it once those who ship it to customers care, is on them to figure out (though note that maintainers will have some burden to review, integrate and maintain the change anyway).
They regularly submit code and they buy consulting from the ffmpeg maintainers according to the maintainer's own website. It seems to me like they're already funding fixes in ffmpeg, and really everyone is just mad that this particular issue didn't come with a fix. Which is honestly not a great look for convincing corporations to invest resources into contributing to upstream. If regular patches and buying dev time from the maintainers isn't enough to avoid getting grief for "not contributing" then why bother spending that time and money in the first place?
Really, the burden is on those shipping products that depend on ffmpeg: they are the ones who have to fix the security issues for their customers. If Google is one of those companies, they should provide the fix in the given time.