2 years and 4 months and 1 week.
Less facetiously, it depends on the guy's physical profile (more highly touted, the easier it is to buy in), their performance profile (good minor league stats or come from nowhere), and exactly how dominant they pitch.
A middling prospect pitching to a 3.50 ERA is gonna have to do it for a real long time before anyone calls him an ace. But a former 1st rounder pitching for a year and a half at 2.50 is gonna get that label from many.
How long would a non-prospect have to pitch at a ~2.00 ERA pace before he becomes an ace? A season? 2? Are we just going to dispense with the labeling untll we trade him for an obvious ace-level haul?