The really fun part of your question is that it's a borderline trick question. That is, there's no public discourse to speak of because the United States has never mandated public education. Due to the 10th Amendment and lack of any mention of education in the Constitution, education is a matter left up to the states. So, to the second part of your question, no the United States wasn't first.

In addition, there is no state in the Union that mandates public education for every child. As a result of a variety of lawsuits in the 20th century, homeschooling and private schools are legal in all 50 states. No parent is required to send their child to public education but a school district must educate every child who lives within their boundaries and presents themselves at the school (or is enrolled by their parent.)

The reason these details are significant is that public discourse around education varied wildly from state to state. The first law related to public education in the American colonies is generally recognized as Massachusetts' "Old Deluder Satan Act", passed in 1647. The law required every town with more than 50 residents to build a school and provide a tutor to the community's children. The law stemmed from religious leaders' fear children weren't sufficiently literate and may fall victim to Satan as a result of their illiteracy. Just a few years later, Boston Latin School was founded, making it the oldest public high school in America. The only children, though, who attended BLS were the sons of White men with access to power or discretionary income.

Which leads us then to the heart of your question. The public discourse around public education is deeply linked to the notion of which children count as members of the public. It's fair to say that American states didn't truly offer public education until 1975 and the passage of the Congressional Education of Handicapped Children Act, later re-authorized as the Individuals with Disabilities Education Act. The law requires all public schools to accept children with disabilities, meaning a school could not turn a child away for having, or thinking they had, a disability. In some states, laws and policies allowed school leaders to explicitly bar children with disabilities. In others, it was more an informal matter where parents would be encouraged to enroll their child in a special school.

And when we're talking about the history of special education, we're generally talking about White children as children of color with disabilities would likely be barred from attending a given public school because of their race, regardless of their disability status. Race wasn't the only way of limiting who was allowed to attend a tax-payer funded school. There were decades in the late 1800s and early 1900s where there were literal brawls between Protestants and Catholics about what happened in public schools. Catholic parents got so frustrated with the presence of Protestant texts in the public schools that they created their own schools, eventually leading to the creation of the parochial school system. The parochial system helped create a template, especially in NYC, for the creation of networks of Jewish, Muslim, and other religious schools.

But back to race. The clearest example of how the notion of "public" shifts depending on where in the country we are can be seen in the state of Mississippi. By the late 1800s, most states in the country had some form of public education and corresponding compulsory education laws. (At the time, this meant children were expected to go to public school. More on the history of homeschooling here.) Most were dead letter laws, meaning they were on the books but not enforced, until the 1920s or so when individual schools fully merged into school districts and created systems for attendance taking and truancy management. (But again, it varies by state. California mostly started with districts while NYS had 20,000 individual schoolhouses that were eventually consolidated into 700 districts.) Mississippi passed compulsory education laws in 1878 but the law made it clear that there were to be separate schools for White and Black children. The funding policies made it clear that schools for White children were to be better resourced and staffed than the schools for Black children. Segregated schools became the norm and around 1920, the law was changed to remove mention of separate schools. However, in the 1950s, when it became clear the NAACP was likely to win its cases related to school integration, Mississippi changed the law again, this time lifting any compulsory education laws. This meant that school and town leaders could refuse to educate any child they wanted; Mississippi schools no longer had an obligation to educate every child who showed up. The law wouldn't be returned to the books until the 1970s. The New York State constitution speaks about a system of "free common schools" so that all the children of the state might be educated. Unlike Mississippi, NYS schools were segregated due to housing policies, not school policies and as such Brown v. Board had limited impact on the state's laws around education.

Virginia provides another example of what "public" means. Following the Brown v. Board ruling in 1954, some counties in Virginia closed down their entire school systems, rather than welcome Black children into classrooms next to White children. We can see variations of this history across the country. In 1885, a California school district refused to enroll a Chinese American child, insisting she needed to attend a school for Asian children. Children in Texas with Mexican ancestry could find themselves welcome or excluded from their town's public school, depending on how the community's leaders felt about Mexican Americans. In places where Mexican Americans were seen first as Americans, it was a non-issue. In places where they were seen as first Mexicans, they were excluded. Similar things happened to German children following World War II.

All of which is to say, the conversation around American public education is tied up with class, race, religion, and a wide range of political issues and is location and context-dependant. In terms of which country did public education first, several European countries arrived at the idea of funding education for the country's children around the same time in the mid-1800s but generally speaking, Prussia is seen as the first country to establish a formal country-wide bureaucracy, teacher training system, and funding structure.