I wouldn't stand for or stand in mud and would start by dumping enough gravel to make the site drain. Build the coop on top of the gravel then add litter.
In most circumstances gravel is a bad option for a chicken run.
While it has it's place in solving severe mud problems (see this article: https://www.backyardchickens.com/articles/how-to-fix-a-muddy-run-chicken-coop.47807/), as a general rule it's more trouble than it's worth because the poop sifts down in, compacts like concrete, and reeks when wet. Also, it's hard on the chickens' feet and can contribute to bumblefoot.
Chunky wood chips are superior.
Choosing a well-drained site and using French drain, grass swales, diversion ditches, and other appropriate water-management is better than gravel.