Bob Armstrong says in his book, Sugar Land, Texas and The Imperial Sugar Company, that W. T. Eldridge, Sr., Stanley Kempner, and other associates leased (for 3 years) the rights to drill for oil on Sugarland Industries property in the early 1920s. Armstrong says they never found oil, but I'm almost certain there were wells on the east side of the Brazos River below Sugar Land. Maybe they weren't on Industries land. I hope to find more on this story.
Regardless, the following newspaper articles announced drilling projects in the early 1920s.
On a lighter note, and probably more appealing to local residents, Sugar Land got an ice cream-making plant. Obviously, it didn't rival Blue Bell.