As SVT-40 mentioned, original A4s have an offset stamping on the receiver so it can be seen when the scope base is mounted. Could yours be a military conversion to A4? Possible but highly unlikely. They had plenty of A4s around so not too many were converted by the military.
The "P" on the underside of the barrel just behind the front sight base indicates it has been proofed fired. Most 1903/03-A3 USGI barrels are marked with the manufacturer (SA, RIA, RA, SC, JA etc) so having one with a P and no other markings is strange.
It could very well be and original SC 6 groove barrel without a marking. IIRC, Early SC are 6 groove barrels. I have an unissued SC 361XXXX with a 6 groove barrel so if your rifle is close to this SN then it would have a 6 groove.
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