Are we talking seashore paspalum? Bermuda? Blue? Rye?
Under near ideal conditions...perennial rye can look really good in 4 to 6 weeks. Top-quality seed, warm soil, lots of water and plenty of fertilizer.
At ideal conditions perennial rye will be 1/4 inch tall at 96 hours.
Bluegrass is a bit slow--sod growers typically allow 18 months to harvest.