Yassar Yaqub, 28, of Huddersfield, was shot when police stopped a car on the sliproad of the motorway on Monday.
The Independent Police Complaints Commission (IPCC) said a gun was found in Mr Yaqub's car. The officers involved had not worn body cameras.
Tests are being carried out by investigators on the two vehicles stopped and an unmarked police car.
Police officers had been travelling in four unmarked vehicles before the shooting.
The car was stopped at Ainley Top near J24 of the M62 in West Yorkshire.
A non-police issue firearm, found in the Audi in which Mr Yaqub was travelling, was secured in the presence of investigators at the scene and is undergoing ballistics and forensic testing, the IPPC said.
None of the police officers involved had been wearing cameras.
So far no relevant CCTV footage of the incident has been found, the police watchdog said.
Derrick Campbell, IPCC Commissioner, said: "I would like to reassure the local and wider community that this will be a thorough and detailed independent investigation.
"We will be carefully examining all the circumstances leading up to Mr Yaqub's death, including the planning of the police operation, and the actions of the officers involved that evening."
Mr Campbell also called for patience, asked any witnesses to come forward and said Mr Yaqub's family were being regularly updated on the investigation.
Dozens of people attended a vigil on Wednesday at the spot where he was shot dead.
About 100 people, including the dead man's parents, gathered near the site to lay flowers and light candles.
Mohammed Yaqub, Yassar's father said he felt his son who he said did not have "a bad past" was "killed unlawfully".
In 2010, Yassar Yaqub was cleared of attempted murder and a firearms offence after it was alleged that he opened fire on a car in Birkby Hall Road, Huddersfield.
On Tuesday evening, protesters carrying banners reading "stop the killings" brought traffic to a halt in Bradford.
A man shot dead in a police operation off the M62 died from gunshot wounds to his chest, post-mortem tests revealed.