I say 6 months if you start in late August in Ohio, have irrigation, top-quality perennial rye and blue mixture, careful soil preparation, perhaps mulch, starter fert according to the results of a soil test, and fert supplemented with a grow-in fert at 4 weeks, 8 weeks, and 12 weeks. Mow early, as mowing at 2 inches encourages the new grass to tiller and grow sideways for thicker results. Early mowing also gets more light down to the soil and encourages the slower growing Kentucky bluegrass with more sunlight.
I am sure the guys that apply hydroseeding have some pictures of lawns that came out beautiful in only a few weeks. How about it Turboguy?
If you are interested in major league baseball field quality, instantly--go with the same sod farm that supplied the nearest baseball field. Costs more--because its better--and weed free.