I obviously don't own anything Harry Potter or Marvel related :)
In 1965, Peggy Carter and Howard Stark founded what would become SHIELD. That same year MACUSA repealed the Rappaport law stating no wizards in America could have any sort of relationship with a muggle, and finally allowed friendships, romantic relationships and working relationships to happen much like they were across the pond in Great Britain. Because of the infancy of SHIELD, they were not introduced to wizards, at least not yet. But a governing body called the Council met with an ICW representative to finally induct North America into a select body of people who knew about the existence of magic, and also why it would be kept a secret, after all, the witch burnings occurred in Salem, and no magical being would forget that any time soon. The relationship between these governments was more a tick box exercise than anything, with MACUSA, the ICW and the American government not interacting much at all for the next 30 years.
After that 30 year period, and an entity known as Captain Marvel crashed back to Earth, the director of SHIELD was given clearance to know about magic, the council deciding to involve wizards to look into the energy readings coming from Carol Danvers to see if it was magic or she was a part of the magical community, however when they tried to contact MACUSA that year, by owl no less, they received no response, and after some deliberation they tried to contact the Ministry of Magic in London. They'd had a good relationship with Nobby Leach who was minister at the time the Rappaport law was repealed, and now had a portrait within the Triskelion, hidden in some random cupboard so it didn't look out of place, but upon trying to talk to the portrait found he could not travel back to his matching one in the Ministry. Finding this odd, but having no way of contacting anyone about it, MACUSA and The Ministry was by and large forgotten about, with the Danvers problem sorted by SHIELD agents. Nick Fury however, did not forget that the first time they tried to ask for help, none was received, and it wasn't until another 5 years had passed that anything came of it.
The portrait of Nobby, finally allowed to move back to his other in the Ministry came back with stories of a second wizarding war with 'muggles' and 'muggle borns' persecuted heavily and large losses across the British Isles. MACUSA had all but closed their doors to the ministry not wanting to incur the wrath of a 'Lord Voldemort' after the events of Grindelwald, and the lack of communication coming from both Cornelius Fudge and Pius Thicknesse during the Voldemort blood war made it impossible for contact, and so the muggle world was left in the dark as Britain and Europe fought to contain the war from spilling over and decimating muggles.
It was a random Tuesday afternoon that Nick Fury found himself talking to a portrait of a man who was explaining their absence and that the new minister in London wished to meet him and give him an easier way to contact them in the future should things once again go south. The following month he met Kingsley Shacklebolt (and wasn't that a mouthful!) who was dressed in deep purple robes and a fez like matching hat, who told him that a teenaged boy had defeated the evil wizard and Britain was no longer at war. MACUSA would have little to do with SHIELD as it was decided by the ICW that the British Ministry would be their point of contact in the future as their government had been around much longer and was closer to both the ICW base and the United Nations. Shacklebolt gave him, yet another portrait, but this one was the size of an A5 piece of paper and intentionally made to look like a picture he'd have on his desk, which infuriated Nick as now people would assume he had a partiality to someone in his life and invited far too many questions for his liking. Shacklebolt eased his mind a little however, explaining that unless someone knew about magic all they would see was a paperweight, which he supposed was fine if it meant not having to explain some random man he had a picture of.
They parted their meeting on ok, if not good terms, with both secretly hoping to never see the other again. Which in hindsight was a terrible way to jinx the events of the future..
A/N- The timeline is similar to cannon but there may be a few years/months here and there slightly different, including a few ages of characters where they are difficult to determine (i.e Steve), and the length of time during the avengers film timeline. For example in the Avengers film it happens over like a week maybe? But From Nat getting Bruce to Loki being captured it will be made to fit this story in a reasonable time for this story.