The Fantastic Four, if integrated into the MCU, could seamlessly be shown not only to exist during this crazy time of heroes,
but to have existed the whole time(and before Iron Man). Some of you have mentioned some of the aspects that would make this work.
As mentioned, The F4 have somethings that the Avengers, Guardians and upcoming Defenders do not.
First, of course, is
Family. Second, and numerically only, is that this is a team of
explorers and
adventurers. Of course they can be heroic, but as unit, they are out to see the world and the universe. Not only that, they are fairly familiar with time travel. Unlike DFOP, Dr. Reed Richards would not disrupt a timeline.
Link contains spoilers
The timeline is the natural explanation of their previous existence. The MCU Earth at this point has several gaps in it
http://marvelcinematicuniverse.wikia.com/wiki/Timeline . The fertile ground here is 1985-1997, as well as 2000-2007.
Having Reed, Victor and Ben around the same age of Stark,Banner and Barton makes a lot of sense. It gives Reed the same intellectual clout as the others and introduces a sort of "Genius Generation" in the MCU. Ben would be an appropriately aged military pilot astronaut, which could include a crossing of paths with other Marvel pilot Rhodes. Sue and Johnny would be around 5-10 years younger than Reed, respectively. If Ben or Reed, based on their talent, are sought after by SHIELD or just simply the U.S. government to travel
space or elsewhere research, explore or build a project in this time period 97-2005. Whether or not they launch to huge publicity, if the project is scrapped or the team is kicked off the project and they steal the vessel are details that can go either way, (I prefer the idea of great fanfare) which leads to one of the main ideas here.
The Disappearing Fight/Mission. Depending on where the go initially, the vessel can vanish. This could be a national tragedy or a government cover up-one that could possibly have been leaked by Black Widow. No one on Earth can find these guys and this becomes the integration point in the larger MCU.
Remember
Dawn of the Planet of the Apes? A newscast referring to the lost shuttle? A simple crumb like that, an anniversary news piece, a reminder of a forgotten problem before the Battle of New York. The reference to the F4 in the MCU in another film or series would be very simple and the F4 are already existing, but where the hell are they?
Where they land and who they find creates the premise of what the hell they've been doing. Whatever that is, the spark of exploration, the sense of adventure, the prospects of being the Columbus, Galileo, Einstein, Neil Armstrong of this century is the opportunity that the F4 can't pass up. So they proceed onward.
The point of origin of the powers can take place before or after the New Mission. The films can follow the adventures, even a spectacular return to the current day Earth in the MCU, their astonishment as well on how much has changed since they left.
Although, aliens have invaded, other realms have threatened existence, AI so advanced that it begins cleansing the earth of heroes, the Return of the Disappearing Mission and what the F4 discovered and achieved would make them the prestigious celebrities they are in the Lee-Kirby spirit. That's how they fit, thats why fit and that's where they belong.