What if we have incorporated as a non-US corporation?
If your company is already incorporated somewhere other than the United States, Canada, Singapore or the Cayman Islands, in order to participate in YC you will need to create a parent company that is in one of those jurisdictions. The existing company will then become a subsidiary of the new United States, Canada, Singapore or Cayman parent company. While lawyers will drive this process, it will require a significant effort on your part.