Using Google, I found several GE refrigerator ads from the early-mid 60's. Saw that handle style used on the '65 models, but for the '66 models, a new handle type was used. Not sure about '64; found an ad from a '64 magazine that showed that handle, but it didn't tell the month, so if late in the year, it could have been for a '65.
The bad thing about relying on ads is that the coming years models usually were introduced sometime between late summer and mid fall. If I had the actual magazine it would make it a lot easier to tell.
Another thing, GE may have still been using older trim styles on some models, especially the lower priced ones, though your model looks to be one that is near TOL.