In 1810, there were only a little over 7 million people in the US, living on 0.02% of the mainland. Since then, population density and urban growth have changed and spread throughout the country, as you can see from this data visualization from cartographer Steven Bernard made from data from Harvard's Dataverse:
It's a fascinating visualization and it shows how transportion infrastructure — first the railways and then the interstate highways in the 20th century — have affected urbanization and sprawl in the US. In the animation, the yellow dots are areas that are highly populated and you can see how the diffusion of yellow dots correlates with the construction of railroads and highways in the country. While most of the highly populated areas were clustered in the east at the beginning of the 19th century, more land has been developed in the past 200 years, spreading from the east to the west.
You can also see from this still image we've grabbed from the animation the different time periods in which cities around the country were built. Land that was developed in the early 1810s is marked in yellow while more recently-developed land is marked out in purple.
And just for fun, here's a tweet from Bernard that shows the spread of urbanization in one unnamed city in the US. From the looks of it, we're going to guess this city is Atlanta, but your guess is as good as ours. You can also check out this Financial Times video with Bernard that provides some additional insights into the urbanization animation project.