Hello,
The LDS possibly could help you with this one. They have the Washington State Birth Index 1907-1954, Births 1907-1948 and Delayed Birth Certificates 1850-1960. Also, they have the Washington State Death Index 1907-1979 and Death Certificates 1907-1960. Does your father think that he was born in King County and/or one of the neighboring counties. If so that will narrow down your search of the birth records. Since he doesn't know his parents names you will have to go thru all the films for the calendar year that he was born, line by line and page by page. This should narrow down your search to a handfull of possibilities. Does your father know if his natural parents died? Another suggestion is the newspapers. Most papers are on film. Check all the papers in the communities that he thinks that he was born in. And what about the hospitals in the area. They should have records on all births born. If your father is still alive, an attorney possibily could help here.
Janet