Where a Polymath means a mastery in much or many areas, an Omnimath means of ALL areas. I do not believe one could become such a title, without an incredible amount of time.
Even still with time on their side, with the changes to knowledge happening at lightening fast paces one might not ever be able to keep up. I know full well that in the future the circumstances may be different, but at our current understanding of knowledge, learning, and capabilities it is near impossible.
I sincerely hope to be proven wrong.
This documentation was created because no other site or person has seemingly talked but it much or at all. There needed to be some sort of document.
One might think that in order to become an Omnimath you would have to spend every single second learning new knowledge, or the downward slope of falling behind will be too much.
Perhaps, or perhaps not. There are ways to automate news and new information to come to you. Creating a "second brain" as some folks in Silicon Valley call it.
NOTE: I am working on my own 2nd brain btw in notion, and when more experience happens with that I will create content based on that. Perhaps that will help you immensely! Either to become a Polymath, or even Omnimath. Who knows!
If one could download information like the matrix or had an endless amount of time #immortal, then perhaps one could be an omnimath.
In actuality though I think two problems would occur.
One like I mentioned above, the knowledge changes so often that it would be impossible to keep up with everything.
Secondly, the problem of information overload. Perhaps in either case there may be a workaround for that, but as of now our brains are limited. Even if they are insanely powerful.