My finch escaped her bird cage outside?

Remember that cats and birds do not mix. The bird cage should be securely hung from a sturdy tree branch and if the door is easily opened tie it with a wire wrap as those used to close plastic bags. Now hang the cage out with the one bird in it as they will tweet to each other. If the other bird comes move the cage to a table at the door then move it in as the bird follows, close the door. I hope it is still near enough to hear the tweet if the bird in the cage.