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I lived in the area of Fairfax and Santa Monica Blvd in LA about 40-50 years ago. I remember seeing a "start route 66" sign just east of Fairfax on Santa Monica Blvd. Could the terminus have been there at that time?
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Several minor changes were made over the years in LA. The original end of Rt 66 was downtown until 1936 when it was extended about 20 miles (32 km) west to the city of Santa Monica on the coast. And then a major change was made in 1953, using the Pasadena Freeway (or CA 110), to bypass a number of downtown streets.
Fairfax and Santa Monica Blvd would be about right for the original point. Still, this doesn't match the 40-50 year time frame you mention. Perhaps you saw a "historical" marker--"Original Starting Point of US 66"--or something like that.
