Is the quickest way to fix knee cartilage surgery?

It depends. It depends on what is wrong with your knee cartilage, what needs to be done, your overall physical condition, and your functional needs. Not all problems require surgery and not all surgery turns out as expected. An MRI can usually demonstrate exactly what is wrong with your knee and those results are then used to determine the procedure that would best fix your problem.
No quick fix. To answer your question, it depends on whether you are referring to "meniscal" cartilage or "articular" cartilage. Arthroscopic surgery can "fix" a torn meniscus quite easily. Damage to articular cartilage however, is much more challenging to treat- there is no way articular cartilage can truly be "fixed" if it is damaged.