There are several variables that affect how long it takes sugar crystals to grow from a water solution.

Crystals form from sugar dissolved in water when the solution becomes supersaturated. When a solution is saturated, it has reached its maximum equilibrium concentration. As water evaporates from a sugar solution, it will become more and more concentrated until it is saturated. Then if more water evaporates, the solution can become supersaturated. When a solution is supersaturated there is a driving force for crystals to form, which lowers the concentration of the solution back to the equilibrium value. However, the crystals must nucleate before crystallization can occur.

Crystals can nucleate from random clusters of sugar molecules that sticks together due to statistical fluctuations, from impurities in the solution like pieces of dirt, or at interfaces of the solution with its container or even at the surface (interface with air). When people grow sugar crystals they sometimes use string or wooden sticks to help nucleate crystals.

Initially the rate of crystal growth depends on the rate of nucleation. Then, after the crystals are nucleated, the rate of crystal growth depends on additional nucleation as well as the rate of evaporation of the water and the surface area of the existing crystals. The faster the water evaporates, the faster the concentration increases. The larger the crystals are, the larger the surface where more molecules can be added. Both of these factors will increase the rate of crystallization.

As explained, crystallization occurs when a solution becomes supersaturated. The solubility of sugar (and other molecules and ions) depends on temperature, so another way to make a supersaturated solution is to cool the solution. As the solution cools, the solubility of the sugar decreases, but the concentration remains the same. Eventually, the solution will reach a point where the equilibrium solubility has dropped below the concentration and the solutions is supersaturated (assuming the solution does not freeze before this happens).

All samples of a sugar solution in perfectly pure water with the same concentration under the same conditions should behave in the same way. However, if there are impurities in the water, they could affect the crystallization of the sugar. Different ions and pH can change solubility which would change the crystallization rate, so adding salt or acid to the water (or using ocean water or slightly acidic rain water) may slightly change the solubility of sugar. Here is what I have been able to find in the published literature about how adding other things to water changes the solubility of sucrose:

- If you add alcohol (ethanol or methanol) to water, sucrose becomes less soluble in the solvent mixture which should cause it to crystallize more readily.

- If you add propionic acid to water, sucrose also becomes less soluble which should cause it to crystallize more readily.

However, having extra molecules in the solution could affect how easily sucrose molecules can reach a crystal surface to add to it, which may slow down crystallization.

You could do an experiment to find if other things in water affect the rate of crystallization if you want to know!

For more information on crystal growth, please see:

References:
Phase Equilibria of D-glucose and Sucrose in Mixed Solvent Mixtures: Comparison of UNIQUAC-based Models. Peres, A. M. and Macedo, E. A. Carbohydrate Research 1997, 303 135-151.

Sucrose Solubility in Mixtures of Water, Alcohol, Ester, and Acid. P. Tsavas,S. Polydorou, E. C. Voutsas, and, K. G. Magoulas, K. Naraghi and, and P. J. Halling. Journal of Chemical & Engineering Data 2002 47 (3), 513-517