Have you never heard of playing the long con?
Sure, the Skrulls work alongside humans while they are desperate. But more and more of them are coming every day. Get some powerful people used to having Skrulls impersonate them when it is convenient, like Fury in Spider-Man, eventually, there's enough of them around, and... "Surely, Director Fury, you didn't expect that we'd be happy living on the outskirts, having no power on our new home planet? You are all desperately inept at controlling yourselves, so... we'll do it for you...."