A monkey using a typewriter could eventually recreate the complete works of Shakespeare just by pressing random keys if you let him go for long enough.

Even if you devise a machine that could reprogram itself with some additional functionality, however minute, and then run a diagnostic to determine if there was some increase in capability and repeat that process forever until the intelligence parameter is maximized, it might take millions of years and a shit ton of computing resources to get anywhere meaningful with todays AI technology. For that approach to work we would need to first meet a certain threshold of general intelligence to make meaningful enough self-improvements to lead anywhere interesting in a timely manner.