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.