In some parts of the United States, there is K4, which is for children who will turn 4 by the end of the calendar year. This means that it is quite possible they are starting into formal schooling at 3y7 (as the school year begins in August).
This hasn't been my experience of schooling in the US.
There are classes called 'PK3' and 'PK4', meaning pre kindergarten for 3 or 4 yos. They are not compulsory. Often PK classes only run three or four days a week, and only for a maximum of three hours per 'school' day. They are attractive to sahps.
In practice, most children go to Kindergarten and a lot of children will spend time in a daycare centre from infancy; a lot of daycare providers have a similar programme to private preK classes, with circle time, reading to the group, art, etc. Most public school districts do not provide preK classes. Private schools tend to, and many also offer all-day care with children brought from a daycare room to their classroom in teh same building for a few hours every day.
In addition to private school offerings and what is available in the YMCA or Park Districts in urban and suburban communities, the federal Headstart Program aims to prepare disadvantaged children for formal school by providing a play-based learning environment, exposure to books and story telling, exposure to normal classroom behaviour expectations, and exposure to the sort of writing and art and science materials they will find in a Kindergarten classroom. The aim is to make up for deficiencies at home that guarantee many children arrive in school with limited vocabulary, no idea what books are for, and behaviour that makes transition to school difficult. Headstart falls short in many ways. Some children have no hope of catching up, and availability of places in Headstart programmes is often limited.
Kindergarten attendance is for children who will have turned 5 by the cutoff date. Most school districts and virtually all private schools provide Kindergarten classes even though very few states mandate attendance in school until First Grade (age 6, and a lot of states only mandate school attendance for children 7 and up).
Up to first grade, what happens in school is very much play based, with each child progressing towards reading at his or her own pace through play, exposure to writing practice, art, singing, being read to, exposure to reading materials, a little phonics and little or no pressure to achieve any set standard. There is a lot of emphasis on the social and emotional aspects of adjustment to school co-operation with peers, and strong encouragement of self-care -- no helping with coats, shoes, lace tying, etc. First grade (age 6 turning 7) is really the start of 'formal' education. Children sit at desks and those who have not yet learned to read will all learn to read at this point, most of the time via phonics plus dolch list (sight word) methods.