Was the Winchester 30-06 introduced in 1903?

No, the Winchester .30-06 cartridge was not introduced in 1903; it was developed in 1906. The .30-06 Springfield, as it is officially known, was adopted by the U.S. Army in that year as a replacement for the .30-03 cartridge. Winchester's Model 1903 rifle, which uses a different cartridge, was released in 1903.