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Cook, 34, signed for Jon Lewis' side following the news the county had been demoted for financial issues by the England and Wales Cricket Board.
They go into Nottinghamshire's visit on Friday with a 48-point deficit.
"Play some seriously good cricket and get promoted at the first attempt - what an incredible story," Cook said.
"That's what you play cricket for, those moments to create history, and a moment of magic," he told BBC Look North.
The South Africa Test batsman arrives at Chester-le-Street for the opening half of the season before joining up with his country for the series against England.
Although his stay is relatively fleeting, Cook is keen to help establish a platform.
"It appeals to me and I know the guys in the dressing room are hugely motivated," he said.
"The hardships are well documented but we've got to use that as motivation rather than an excuse."
Moving to Durham has allowed Cook to follow in his father Jimmy's footsteps, having spent the rest of his career in his native country with Gauteng and Lions.
"To play county cricket has been a lifelong goal," Cook continued.
"Ever since I was a young boy, it's the whole tradition and splendour of it all.
"My dad played for Somerset many a year ago, I watched him from afar and always liked the idea of it.
"He had a really successful time of it and if I can do half of that I'll have an enjoyable summer.
"To be able to finally walk out there on Friday will be a great time for me."

The plane was heading from Heathrow to Dubai on Thursday - a seven-hour flight.
Abhishek Sachdev, who was on board tweeted: "Insane. Our BA flight to Dubai returned back to Heathrow because of a smelly poo in the toilet".
He told a newspaper: "The pilot made an announcement requesting senior cabin crew, and we knew something was a bit odd.
"About 10 minutes later he said 'You may have noticed there's a quite pungent smell coming from one of the toilets'.
"He said it was liquid faecal excrement. Those are the words he used."
The plane had been airborne for just 30 minutes when it turned round.
The next available flight was 15 hours later, so passengers had to be put up in a hotel overnight.
Speaking to Radio 1's Greg James, Sarah, who works for the airline said: "When you're up at that altitude the cabin has to be pressurised so the problem is that anything like that is actually a health and safety problem because only 50 percent of the air is being recycled and cleaned".
In a statement, BA says "A decision was taken to return for the safety and comfort of our customers on board.
"We're very sorry for the discomfort to our customers.
"We provided them with hotel accommodation and rescheduled the flight to depart the next day."
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Durham's bid for promotion to County Championship Division One despite a points penalty is a "wonderful challenge", says opener Stephen Cook.
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A British Airways flight was forced to turn around because of a "smelly poo".