Strictly speaking knowledge is immense, but not infinite, as it is the result of Mankind's
intellect, acting over a long but not infinite amount of time (history, or prehistory plus history).
The unsolved questions or unknown things might be infinite, and if they are infinite
they will always remain infinite, as Mankind (always a huge but finite aggregation of men and women) could only turn finite amounts of
those questions into knowledge; of course the right questions should also be raised, before conquering anything.
Another possibility could be the discovery of general formulas and relations by which :
a) producing questions
b) producing the answer related to a question via a finite collection of algorithms
In this manner we could theoretically list any (finite) amount of questions and
automatically produce the answers; I believe this possibility has been explored by the great English mathematician Alan Turing (who by the way gave a significant
contribution also in defeating the Nazis in WWII) and the result is that it is impossible
(I'm not sure if I'm reporting the result correctly). Also Godel gave important tributes to this kind of questions.