BOCA CHICA, Texas – To Gilberto Salinas, the gleaming glass-and-steel building with the “SPACEX” sign emblazoned across its top stretching along State Highway 4 represents a portal into the future – a doorway to deep-space exploration just a few miles from his home.

Just down the road, workers mill in and out of the launch pad area where SpaceX founder Elon Musk and his team propel 5,000-ton rockets into outer space and from where the tycoon hopes to someday send humans to Mars.

“I still get goosebumps when I see those rockets launching,” said Salinas, chief executive of Brownsville’s economic development arm. “The future of deep-space exploration is happening here in our backyard.”

An entrance to ...