This is a popular topic lately!

In effect, children* have been taught American history since pretty much the beginning of America. From a previous response to a similar question:

Introduction to the History of America: Designed to Instruct American Youth in the Elements of the History of Their Own Country was published in 1787 and is generally recognized as the first American textbook. The author took passages from texts written for adults on American history and re-purposed them for young readers.

The book was used by colonial teachers/tutors during lessons but a class devoted to the study of American history wouldn't become a feature of a child's school day until much later. The concept of silo-ed classes (i.e math class, history class, science class, etc.) became the norm around the 1910's. There were a variety of factors that lead to the development of classes as we think of them - this response gets into how they all came together.

*Children being white boys, sometimes girls. Education for enslaved children was rare and forbidden by law in more states than not until after the Civil War. Native or indigenous children's school experience generally focused on converting them to Christianity.