Aerial photos of Oakmont from the mid to late 1920s don't show any paths between tee and fairway. It may be that Hogan helped Oakmont change their maintenance practice, but they clearly existed long before 1953 at other courses.
I looked through a lot of old aerial photographs (thanks, Craig!) and while all didn't have them, many clubs in the late 1930s had mowed lanes from tee to fairway. Chicago GC, Creek Club, Doylestown, Elyria, Huntingdon Valley, Indian Creek, LuLu, Merion East, NGLA, Norfolk CC, Philadelphia Cricket among many others had them in the late 1930s.