Kenneth Adelman has had to learn to be patient.

An electric-car enthusiast and retired “computer geek,” in February 2012 he was the first person to plunk down a $40,000 deposit for Tesla Motors Inc.’s Model X sport-utility vehicle. At the time, Mr. Adelman didn’t know the Model X’s total price, but Chief Executive Elon Musk said the vehicle would be in his hands by the end of 2013.

He is still waiting. After nearly two years’ worth of delays, Tesla kicks off Model X deliveries Tuesday. Although first on the order list, Mr. Adelman, 52 years old, doesn’t know when he will get his vehicle and he is showing little concern.

“I’m happy to have waited for the X to be all that it could be,” Mr. Adelman, who also owns a Tesla Roadster and Model S sedan, said in a recent interview. He is confident the vehicle is a “home run.”

Topping out at $132,000, the Model X will test the Silicon Valley electric-vehicle company’s ability to preserve momentum that has been largely unaffected by low gasoline prices and turbulence in emerging markets. Tesla is banking on the new vehicle to help it to achieve sales of at least 50,000 vehicle in 2015 and 500,000 by 2020.