How long grass takes to germinate depends on the type. Fescue will take 7-10 days, while blue grass can take 21 days.
Trying to establish a lawn at this time of year in Ohio is extremely difficult. You have the worst of everything. Increasing temps, strong competition from weeds, crabgrass germinating, the likelihood of periods with little rain and high temps ahead, etc. And these are cool season grasses, which want to grow agressively in fall and spring, not the high heat of summer. IMO, for any decent size lawn, unless you have inground sprinklers and water is free, it's just impractical to be able to successfully establish a lawn from seed now.
Watering once a day from the start might be sufficient in mid Sept or April, but it isn't going to give good results now. The surface of the soil needs to be kept constantly damp for the first several weeks. This time of year, that means watering several times a day. Somewhere around 11am, 3pm, then 8pm would be good. It doesn't have to be deep, just enough to keep the surface wet. As the grass comes in, you can gradually back off the watering frequency, but increase the duration, so you water deeper.
In all, you may be better off just giving up on what's there with the plan to kill off everything in early Sept, then reseed. This also gives you the ability to use quality seed, instead of the typical cheap crap that a builder will throw down.