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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."
Durham's bid for promotion to County Championship Division One despite a points penalty is a "wonderful challenge", says opener Stephen Cook.