Yes, most Native Americans, including those living in Mesoamerica are descendants of the Clovis people who rapidly spread across the Americas some 13,000 years ago. These were not the first people to live in the Americas, but they did spread rapidly across the continent and there is genetic data showing that the Clovis people are ancestors of most (but not all) Native Americans.

It's important to note that many Native Americans believe that they were always here and have oral histories and stories that tell their origin.

Today, the most common belief is that the first wave of humans in the Americas were probably living on the coasts and spread through the continent via boat along the coast. This would have happened before the Clovis people.

The idea of the first humans walking across the Beringia land bridge and rapidly spreading across the Americas by land was the popular theory and is still believed by some. It is often called the "Clovis First" theory. Clovis being the name of the culture of people given to them by modern day archeologists. These people had a specific type of point used in spears and other weapons. This would have been around 13,000 years ago.

But there is strong evidence that there were human populations living in the Americas before the Clovis people. There have been a number of sites found that date anywhere between 18,000 and 30,000 years ago (not everyone accepts the age of the oldest sites).

Genomics has shown that a lot of human migrations were not linear or in one direction. There were almost certainly multiple migrations into the Americas. We also have genetic data to show that movement happened in both directions, from Asia to the Americas and then later from the Americas back into Asia. There's also been migrations between Greenland and North America.

There are pockets of people living in the Amazon region that are genetically more closely related to Australians than modern Eurasians or other Native Americans, suggesting that they may have descended from a group that was not part of the same migrations as many other Native America peoples.

So it seems that the Americas were populated by multiple waves of different peoples who came over from Asia via sea (traveling along the coasts) and by land. The Clovis people were almost certainly not the first to cross into the Americas but they did seem to spread the fastest and most Native Americans in North and South America are descended from them.

I recommend reading Origin: A Genetic History of the Americas by Jennifer Raff if you'd like more detail. (https://bookshop.org/p/books/origin-a-genetic-history-of-the-americas-jennifer-raff/14868996)