BOCA CHICA VILLAGE, Tex. — As you drive east along Texas State Highway 4, it looks like a giant, shiny and pointy grain silo is rising out of the scrubby flatland at the tip of southern Texas.

But it is the first version of a spaceship design that Elon Musk, the entrepreneur and founder of the rocket company SpaceX, hopes will be humanity’s first ride to Mars.

Within a month or two, he says optimistically, this prototype of the Starship spacecraft — without anyone aboard — will blast off to an altitude of 12 miles, then return to the ground in one piece.

“It’s going to be pretty epic to see that thing take off and come back,” Mr. Musk said late on Saturday at a SpaceX facility outside Brownsville, Tex., where Starship is being built.