An Instagram user shared a video of the electric truck being followed by a Tesla Model 3 on a street in Hawthorne near SpaceX's California headquarters.
Tesla and SpaceX CEO Elon Musk revealed on Wednesday that more than 250,000 pre-orders have been placed for the Cybertruck, though he is yet to reveal when the exact release date will be.
Pre-orders require a $100 downpayment, meaning Tesla has generated more than $25 million within the first week of its unveiling.
Production for the futuristic vehicle will begin at some point in 2021, he said, with orders being fulfilled later that year or in early 2022.
At the unveiling of the Cybertruck last week, Mr Musk described it as unlike any pickup truck that has come before it.
"Trucks have been the same for like 100 years," he said. "We need something different and we need sustainable energy now. To solve sustainable energy we have to have a pickup truck."
It comes with impressive specs, capable of accelerating from 0-60mph in under 3 seconds and towing heavy loads.
Tesla claims it offers "better utility than a truck with more performance than a sports car", and pulled several stunts to attempt to prove it.
One involved throwing a metal ball at the windows of the truck during the unveiling event in an attempt to show off the strength of the armoured glass. An apparent mishap meant two windows of the Cybertruck were damaged.
In a separate video demonstration, Tesla showed the electric truck beating a Ford F-150 pickup in a tug-of-war contest.
Executives from Ford have since claimed the test was not carried out under fair conditions and challenged the electric car maker to a rematch.