Houston Independent School District (HISD) had purchased West End Park from the Houston Buffaloes when they moved into Buffalo Stadium in 1928. The ballpark, which was also used for football and other athletic events, had originally been constructed in 1904, and was in need of replacement. It was because of this that a larger, modern venue began being planned by school board officials.

Prior to the construction of Robertson Stadium, the University of Houston campus had been built nearby in 1939. In March 1940 the HISD, who were in control of the university at the time, purchased the undeveloped site for a stadium from the Settegast Estate for $75,550.16. Another 7 acres (28,000 m2) was acquired soon thereafter to bring the original site total to 59.7939 acres (241,977 m2). The area of land is now bound by Holman Street, Wheeler Street, Scott Street, and Cullen Boulevard.

The stadium was then constructed as a joint project between HISD and the Works Progress Administration by the Fretz Construction Company. Named the "Public School Stadium", it was completed in 1942, and had a seating capacity of 14,500. Public School Fieldhouse (later known as Jeppesen Gymnasium), a multi-purpose indoor arena which was constructed simultaneously, stood alongside. The stadium's first game was held before a crowd of 14,500 on September 18, 1942, when Houston's Lamar High School defeated Dallas' W. H. Adamson High School 26–7.

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