It says quite clearly on the TIN sheet document that you can use your UCN as TIN, which will be your Foreign tax identification number.
However, since you are operating as a company, in this case you will be required to request ITIN from the IRS as others have done. Process takes some time. The french residents for example have had to go this route as they do not have a TIN and is the same in case you are operating as a company from what I’ve read around.