The TransAm has been run for decades, and there were even races in the 1920s (the famous "Bunion Derby") and again in the early 1990s. A web search will yield much history, here's a brief summary: https://www.outsideonline.com/2129171/brief-history-run-across-america The course is open, and of course evolves with development of the road system, but the end points are fixed: City Hall in San Francisco and New York City Hall (note that the TransAm footraces were Los Angeles to New York).
In 1980 Frank Giannino set the record for the TransAm that would last for 36 years, at 46d8h36m. It was broken by Pete Kostelnick in 2016. The women's FKT lasted even longer. According to Ultrarunning Magazine: "That record had been immovably standing since 1978, when South African Mavis Hutchinson ran from Los Angeles to New York City in 69 days." (Actually, 69d2h40m) It was finally broken in 2017 by Sandra Villines, by over 2 weeks!
Note of Dec. 7th 2023:
It is worth to mention that senior (75 this year) runner Björn Suneson of Sweden has crossed the US 8 times by now. He also maintains a record of crossings (walking and running) since 2012 in an excel format that is regularly updated. His homepage is here (you can use google translate to translate from Swedish if you need to).