How many years of growth does it take before a paw paw can produce fruit?

If you mean the Carica papaya, then in tropical climates this can be as little as 9 months from seedling stage to flowering. This extends in proportion to distance away from the tropics to become about 18 months in warm temperate regions. The taste of paw-paw also deteriorates in proportion to how far from the tropics the fruit is produced. .