The A&M College of Texas
The school now known worldwide as Texas A&M University, was first conceived in 1866. That year, the Texas state legislature accepted provisions of the Morrill Act, in which the United States Congress established "land-grant colleges" from the sale of federal lands and mandated investment accounts from the proceeds of those sales to provide for a permanent endowment to these newly-formed institutions. Signed by Abraham Lincoln in 1862, the Morrill Act called for these schools to emphasize agricultural and engineering curriculum, as well as provide instruction in military tactics.
On April 17, 1871, the Agricultural and Mechanical College of Texas was established by the Texas legislature. Appropriations of $75,000 were earmarked for construction and to hire faculty and staff. Some four and a half years later, on October 4, 1876, the school was dedicated on a site approximately five miles south of the town of Bryan, TX.
Meanwhile, a search continued to locate the state's "main university" which had been mandated in 1839, prior to statehood. That search finally ended in 1881, when a site for the University of Texas was chosen in Austin. That school opened its doors to students in 1883.
So, yes, Texas A&M University was the state's first institution of higher learning. It's first president was Thomas E. Gathright. Electricity came to the campus in 1890, and the school's first football game was played on November 30, 1894. On that day, the host team defeated Ball High School of Galveston 14-6.
And a lot more has happened since then.