According to this link the serial number cut off for post 64 starts with 2,700,000. Since 1963 ended with 2,586,000, they have a note that serial numbers 2,586,001 through 2,699,999 were not used.
model 94 serial numbers
P.S. The things to look for with the post 64 models
The Frame was no longer machined, but but cast from a powdered steel alloy. Consequently the new alloy required a different chemical to blue it and it never looked quite right compared to the barrel and magazine, which were still blued using the traditional hot salts Winchester had used since before the war. The difference in the finish of the receiver and the barrel/magazine tubes is usually pretty obvious.
The butt plate was changed from checkered steel to hard molded plastic.
The loading gate and shell lifter were changed from machined steel to stamped sheet steel.
There were other minor internal changes, but one would have to disassemble the gun to see them.
Note: I should add that Winchester may have had some of the machined pre-64 components on hand at the start of 1964, which they would have continued to use until they ran out. Consequently, some of these parts might show up in early 1964 production.