Yeppers. I wholly agree about levels of ambiguity with the term "first families." Not really in scope for this thread, but I think in this instance much revolves around the unique history of Texas itself. You see, there was never an entity or territory called Texas until the Republic of Texas declared itself...which is another technical rabbit hole as to dates. But...
Starting at the beginning, there are no written records from indigenous, pre-Columbian Texas. Those, of course, would truly be the first families of the region, but the only record is archeological. The earliest skeletal remains discovered in the region was the so-called "Leanderthal Lady"...named not for relationship to those other ancient European hominids, but because the remains were discovered, in 1983, near the town of Leander. I had no involvement, so can't be blamed for the groaner wordplay. :-) The remains, with carbon dating and analysis of geological stratification, were placed at between 10,000 and 13,000 years old.
Spanish explorations into what is now Texas began, sporadically and sparsely, as early as 1519. The first European...resident presence, I suppose you could call it, was established in 1680 along the northern bank of the Rio Grande River, not terribly far from what today is El Paso. These were actually excommunicado Spaniards and some Native Americans who had fled there after what's called the "Pueblo Revolt" in today's northern New Mexico. So this wasn't an official emplacement.
Shortening the story, the region was nominally under French control from 1684 through 1689; the small "Fort Saint Louis" had a French flag planted in the ground in 1682 near today's Matagorda Bay, before the establishment of New Orleans. But after three years the fort was no more, reclaimed by the Native Americans who lived in the region.
With the French growing their presence around the mouth of the Mississippi River, and with small, temporary excursions farther down the Gulf Coast, Spain felt pressured to once again try to "settle" parts of the region in order solidify their claim to the land over France. The first attempts, circa 1691 in the east, near the Louisiana border, flopped and were abandoned.
It was 20 years before Spain again gave it the old college try, and over the next century they established a small number of missions and presidios in the region. Most of the "colonists," though, were soldiers and missionaries; very few actual settlers arrived to attempt to make homes in the new land. But the area was nominally Spanish from 1690 to 1821.
The Mexican War of Independence saw its first shots in 1810. In what amounted to assistive incursions, a number of Anglo Americans fought on the side of Mexico against Spain; one of the largest cadres of these guerilla Anglo units, part of the so-called "Republican Army of the North," consisted of over 130 men who fought under Bernardo Gutiérrez de Lara and the Anglo Augustus Magee. In 1813 (here comes the technical rabbit hole) after a victory at the Battle of Rosillo Creek, the Republican Army of the North declared an independent "Republic of Texas" and named Gutiérrez de Lara its president.
That was in early April; it screeched to a halt only four months later when the Spanish army crushed the Republican Army of the North at the Battle of Medina. So technically that was the first time the word Texas was used to denote a geographical and political entity. Some of the veterans of that deciding battle would, two decades later, go on to become signatories of the Texas Declaration of Independence. The notion of an independent, sovereign Texas continued to simmer--and even percolate once in a while in skirmishes--during those 20 years...and to be clear, this wasn't a purely Anglo American thing; key leaders and fighters in the push for Texas independence were Mexican.
So...Mexico won its independence from Spain in 1821 and declared a constitutional monarchy under Emperor Agustín de Iturbide. The empire only made to 1823 when Iturbide was ousted and replaced by a republican form of government. In 1824, with its capital placed as far as possible south of the Rio Grande, two very sparsely populated areas were combined to form an official Mexican state, the State of Coahuila y Tejas.
The State of Coahuila y Tejas was the first formal apportionment defining the area, part of which would become Texas. And as of that point we're now into the timeframe covered by the "Texas First Families" designation. And there was still no "Texas," per se...er, ignoring the four months in 1813 when nobody recognized the claim of the Republican Army of the North anyway.
By 1834/35 the number of Anglo permanent settlers in what would become Texas greatly outnumbered the number of Mexicans. But considering the expanse of our state, the numbers were infinitesimal: a bit over 30,000 Anglo settlers to about 7,800 Mexican counterparts.
The Battle of Gonzales on 2 October 1835 was the first engagement of the Texas Revolution, and the start of what would become the sovereign Republic of Texas for a decade before an agreement was reached to admit the country into the United States as the State of Texas.
But now that I feel like James Michener--who really did write a novel titled Texas which, come to think of it, I haven't read since it came out in the late '80s--I did say that the reasons for the term "Texas First Families" was above my pay grade and really not in scope here because the WikiTree Category and sticker defining the particular timeframe and criteria already exist.
But ya really can't take a Texan anywhere. Because if someone asks why Texas is different, the darned Texan will start telling you about it until everyone else leaves the party...