It Was The Americans Who Broke Through

From Lots of Land:

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But, by and large, Spain never attempted to settle Texas, only to guard it, to keep anyone else from grabbing it.  As Mattie Austin Hatcher wrote...,

The Spaniards felt compelled to be on their guard against...the Americans, whom
they feared most of all. 

The latter premonition proved a wise one. Spain had held her own against the French, had maintained at least a formal authority over the Indians, was able to reduce the Louisiana immigration to only a trickle, and had completely shut the English.

It was the American who broke through the closed door.  He was on his way by the end of the century, when Nolan had already captured wild horses (and perhaps drawn his maps for General James Wilkinson) west of the Red River.