Using Googlebooks, I came up with a 1960 (date verified) government document, “The Role of the Department of Commerce in Science and Technology: a report to the Secretary of Commerce by a special advisory committee of the National Academy of Sciences.” It uses the phrase “mission statement” several times. Here is the first:
3. The existing mission statement for Radio Propagation and Standards should be issued as an Executive Order. A similar statement for Data Processing should be prepared, evaluated and, if found appropriate, given similar status.
I also found Therapeutic Food Manual by Royal Lee, DDS, published by the International Foundation for Nutrition and Health, which prominently contains a Mission Statement for that organization before the table of contents. Google dates this book at 1953, and the copyright page shows the same date, but it also shows an ISBN number for the book and a fax number, website, and email address for the organization. So I think that this particular edition was not printed in 1953, and don’t trust that as a date for the mission statement.