Exactly. The most common rebuttal I’ve heard to this is that the word “democracy” doesn’t appear in the U.S. Constitution. However, other ideas like “freedom of religion” and “separation of powers” also do not appear as exact quotes in the Constitution.

Instead, the concept embodied by these phrases do exist and are written into the very fabric of the Constitution.

Here’s a link which explains it best: https://www.thoughtco.com/republic-vs-democracy-4169936

The United States, while basically a republic, is best described as a “representative democracy.”

Also, back in the founders era, they would have understood democracy to mean what we today consider direct democracy. They thought that was too messy (to have every citizen vote on every new law etc) which is why went with a slightly different model. So they went with representative democracy instead of direct democracy. Even the Electoral College technically fits with this definition - we use the statewide popular vote (direct voting) to pick our representatives, the electors, who will represent us in the vote for the US President and VP. (Except for the two states that do it by district and split their EC votes, but in that case it’s the district wide popular vote that picks the representative.)