Was the US formed as a democracy or a republic?

This is a good question as the term democracy and republic in modern days are used to describe many different political organizations. Often they were used interchangeably. The Pew Research Institute survey in 2017 concluded that six of every ten countries are some form of democracy. The United Nations reports of the approximately 192 countries that are members, 123 of the countries claim to be democratic. When we examine the term democracy as pictured by the American public, it differs in form from our close ally in Great Britain. Let's examine the question from a historical perspective.
Democracy and democratic is a Greek term that literally means rule by the people. Recall that in the earliest days of colonial America, Great Britain was beginning a transition from the absolute rule of the monarchy to a parliamentary form of government. The American colonists were considered under the authority of the monarchy though white male property owners were allowed to vote on matters concerning the administration of the colony. Early in the founding of the colonies was the notion that people most affected by the government should have a say in how the government was run and who was in charge. As the Americans began to move towards independence from Great Britain, a great deal of thought went into how to best achieve rule by the people in a pragmatic and practical way.
Democracies are characterized foremost by free elections without interference by the government. Direct democracy is when citizens vote on every issue affecting them. While voting by citizens in town halls and local community meetings worked when the colonies consisted of a few hundred people, holding a vote on every issue of government was not practical. As the colonies enlarged, so did the need for a bureaucracy that could act on behalf of elected representatives without the necessity of a citizen vote for every single matter. The founders were keenly aware and able to observe what was happening in Europe as monarchs began giving way to democratically formed governance. It is not a coincidence that many of the founders were fluent in Greek and Latin as well as being educated in world history, in particular, the history of the Roman and Greek empires. They were equally familiar with the philosophers from Great Britain and France that predicted the decline of monarchies and the rise of democratic institutions.
The word republic is a Latin word meaning a public thing. A republic is a form of government whereby citizens have a say in the government, and the head of state is not a monarch. The key to a functioning republic is the confidence citizens have in their elected leaders to represent and act on issues impartially. Keep in mind in our current time; many countries claim they are democratic or republics. For example, North Korea and China use the word republic to describe their states. Neither is democratic. In the historical context of the founding of America, there is no comparison to what is currently termed a republic or in some cases termed as democratic.
When the founders began thinking about how to completely banish the notions of a monarchy and retain the democratic ideals expressed by the town hall meeting whereby citizens input was coveted, the form of American democracy took a turn different from Great Britain's parliamentary government. In America, the founders were able to combine the ideals of democracy with the practical elements of a republic. A republic form of government is one made up of elected officials acting on behalf of an active voting citizenry. A democracy is a form of government where citizens express their views through voting for elected officials to act on their behalf. The term representative government is also used to describe how the colonists wanted to be governed. Principles found in the republic and direct form of democracy are evident in the historical writings of the founders of America.
From a historical perspective and there is a great deal of debate as to which position is correct because initially (As evidenced by the Declaration of Independence.) the primary interest in the founders was to disassociate the colonies with a monarchy form of government, the idea of a republic form of government may have been the first organizing principle. However, since voting was a key component of colonial life, it is hard to fathom how democracy was not the cornerstone of the republic. Reading the writing from the early founders leads to the conclusion America evolved into a democratic republic, and the United States is the realization of the vision of the founders.
https://www.nationalreview.com/magazine/2018/10/01/democracy-or-republic/

https://www.theatlantic.com/magazine/archive/2018/03/america-is-not-a-democracy/550931/