Modify the soil/thatch layer as much as possible-Drill and fill, vertidrain, core aerify and graden. That's the first year. Get on a hand watering program. I have never been a fan of deep and infrequent, unless trying to flush salts. Handwatering drives roots and keeps the surface firm day in a day out. I always felt and deep and infrequent watering program made for 2-3 days of very soft surfaces and depending on the climate, you may not want to have wet greens very long. As stated, there are SO MANY variables to this with modifying the soil being #1. With the proper programs and the acceptance of sub par surfaces around aerification, very good green speeds are likely. You will not have dirt with a good watering and topdressing program. The more sand in the canopy, the smoother the put and TO ME, the higher height of cut can be utilized and believe it or not, faster greens. We do not have to mow ultra low here but are consistently 12.5+. The membership has backed our program and we have healthy, firm, grain free greens.