The incident happened around 6am on Saturday on the A737 near the junction with Barrmill Road.
The vehicle, a black Renault Megane, was traced on the B777 between Beith and Longbar at around 6.15am.
One suspect is described as being a man, around 6ft tall, of medium build wearing dark clothing and a black baseball cap. The other is described as being a man, with medium-length black hair and stubble, also wearing dark clothing.
Detective Constable Lee Duncan said:
“Our inquiries are ongoing and we are appealing to anyone with information to contact us.
“We also ask any drivers in the areas at the time with dashcam footage to come forward.”
Anyone with information is asked to contact police on 101 quoting incident 0769 of 16 March 2024.