Because the age of compulsory schooling is six, yes, you can skip kindergarten in New York and start with first grade at age six.
However, many five-year-olds benefit from a gentle dabbling into more formal schooling. So you are free to teach kindergarten at home as a homeschooler. And the upside is that there’s no regulation at this stage or at younger levels like preschool or pre-K. You can do preschool, pre-K, or kindergarten at home without notifying the state or filing any paperwork.
Choose an age-appropriate curriculum that nurtures your youngster’s natural curiosity and instills a love of reading. Here are three choices to consider before compulsory schooling at age 6:
Preschool Package: Fiction, Fairy Tales, and Fun for ages 3-4
Pre-Kindergarten Package: Exploring God's World for ages 4-5
Exploring American History: History / Bible / Literature K  for ages 5-7