1903s from 330000 to 340000 were all made in 1908, unless it was made by Rock Island, and then it was 1919. Either way, that would be a 1903, not a 1903A1 or A3.
Know that, if your gun is a Springfield, it is a "low numbered" rifle, and is considered unsafe by many people. The magic number for safe and unsafe, for Springfield, is 800000. If, however, your gun is Rock Island, the magic number is 286506, so yours is considered safe.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
I always take precautions.
Beware the Evil Bullet Fairies.