Surely the State does, even if the public does not?
Nope, how would they get access other than a taking of private property? We're talking the "wild west" out here.
some google info
"Before Wyoming achieved statehood in 1890, the distribution of private land was shaped by federal policies and land grants. The federal government took land from tribal nations through treaties, often not upheld, and divided it into one-square-mile sections, initiating a complex ownership pattern. To encourage railroad development, the federal government granted the Union Pacific Railroad every other square mile for 20 miles on either side of its route, creating a checkerboard pattern of private and federal land. This resulted in the railroad becoming the largest private landowner in Wyoming by the 21st century, holding millions of acres granted in the 1860s.
Additionally, the Homestead Act of 1862 allowed individuals to claim up to 160 acres of federal land by living on it, improving it, and farming for five years. This act attracted numerous settlers, especially along fertile riverbanks, leading to the establishment of small farms and ranches. The Preemption Act of 1841 also enabled settlers to purchase up to 160 acres at $1.25 per acre, further increasing private land ownership.
Veterans were given land scrip after wars, which they could exchange for land in the public domain; however, many sold their scrip to speculators who consolidated large land holdings, removing vast tracts from public availability at low cost. These mechanisms—railroad grants, homesteading, preemption, and veteran land warrants—were central to the transfer of land from public domain to private ownership in Wyoming before statehood."