The first season of Stargate Atlantis has always been my favorite because they were separated from Earth and "trapped" in another, hostile galaxy.
I have been thinking through AU methods of keeping them out of contact with Earth longer. The problem, though, is the ZPM and the shield. In order to last against the Wraith they need the shield. But if they have a ZPM to power the shield, then they could dial earth.
I came up with one idea, all based on the fact that the Atlantis Stargate is the only way back to Earth. If they were forced to disable this functionality (before getting a ZPM), in order to keep the Stargate from falling into the hands of the Wraith in a way that is hard (if not impossible) to fix, then they could acquire a ZPM and still not have the ability to contact Earth. In this AU, they would never have sent the data stream to Earth.
Another possibility is that they find a ZPM at the last min when being attacked (not enough time to contact Earth) and it is drained in the defense of Atlantis. Leaving them safe from the Wraith attack at the end of Season 1, yet back to where they were before they found the ZPM. In this version, the gate would still be capable of dialing Earth and they probably would have sent the data stream to Earth.
They would contact Earth eventually, or Earth would contact them eventually, but maybe not for several years.