This, of course, depends on their reason for studying us in the first place. Are they just scientific minded (in an alien sort of way)? Or perhaps they want to help us along and have good intentions for human civilization? They could also have ill will towards us of some sort? The motivation for First Contact is essential in any scenario. It ultimately would direct how they might respond.
So perhaps they do have our best interests at heart. What might cause them to step out of the wings and say hello? If they really do care what happens to us, then perhaps it would come down to what they think might happen to human civilization in event of First Contact. From our extremely limited perspective it could certainly appear that western civilization is on the ropes and democracy is facing a huge challenge. Will our economic woes lead to the failure of the American dream? Do the aliens even give two damns about the American dream? Who’s to say the Chinese model doesn’t make more sense to them? But let’s say they do care about democracy and the freedom of the individual being. What would provoke them to say hello?
I can think of a number of reasons they may want to do contact us. The first would be to shock our economic system back to life. If the U.S. economy goes flatline, the mere appearance of extraterrestrials could jump start the global economy. Suddenly, there would be all sorts of economic opportunities. Investors might see a reason to re-enter the market to try and capitalize on what could be the next big things: space development and cutting edge technologies. Banks could be more likely to loan money as new ideas enter our system. A little alien information could be a big boost to the faltering world economy. The next reason could be that extraterrestrials do give a damn about individual liberty and freedom of information. As many problems as we have in the United States, we have about the best system on the planet for continuing these human freedoms. Extraterrestrials may not be American supporters per se, but they could support the ideals we stand for, no matter how much we might trample them ourselves. The third reason could be to interject themselves into a larger philosophical war, one that we can’t fully see, due to our limited perspective. The rise of religious fundamentalism is a global phenomenon. It’s happening all over the world, including in Muslim, Jewish and Christian sects. Perhaps there is a larger battle occurring between secular-scientific thought and regressive religious thought, and perhaps they are worried about how it might turn out for us?
Much of this line of thought is wishful thinking on our part. It would be swell to have extraterrestrials come and help us solve our problems. There have certainly been points in human history where civilization was much more endangered. World War Two and the Cuban Missile Crisis are two examples. Aliens didn’t show up then, so why should they now?
It could be that from the alien perspective it’s not so much a case of humanity on the ropes and needing help, as it is humanity in an important phase of development. Despite world economic woes our technology has drawn us together, the threat of all-out nuclear war has lessened considerably in recent years and we are showing signs of greater global cooperation. Maybe we’re ready and that is their only consideration? They may have just been waiting for us to grow up.