a year, maybe. depends on how much light it gets, and how much nitrate and CO2. mine went from the size of a fist to the size of a football in 3 months.
In good conditions even in lower light no co2 added tanks java moss can double in size every couple of months. With nutrients lacking its growth can be slow to the point that it would take a year or more to double if algae doesn't choke it out first.