Yes, I believe it is possible - I believe I have done it, several times, and against the odds as well.

Manifestation for me is about holding a vision and trusting 100% it will come about. I also learned a long time ago that the "how" of something will come about is the bit that should be left to the universe, and in the meantime my focus should be on how things will be when the vision manifests - how I will FEEL, what my experience will be.

It's important to be clear about what you want and set your intention very clearly to the universe, whether verbally or on paper (I suppose this is a form of cosmic ordering).

It's also important to be grateful - gratitude energy is such a positive force for manifestation. As loa1209 says above, gratitude is also a daily practice, at its most potent, and remembering to be grateful for things that seem like small things to some of us but to others in the world they would be huge (food, clean water, shelter, safety). I try to say thank you to the universe for the things I ask for at the time of asking - demonstrating 100% trust that it will be.