Depending on what is meant by 'programming,' computer science really grew out of mathematics and occasionally physics departments at colleges in the late 50s and early 60s. Disciplines started establishing CS departments in the US around the mid- to late- 60s. I'd say anyone exposed to that period on could be considered as having formal training in "programming" in a college or university environment.

I have a good friend that worked during the 60s era programming with punch cards doing applied physics work in FORTRAN (pre 77) which was already pretty big by then. You could probably go back a bit further but I don't think much was being actively taught as a sort of course one might expect today then. So I'd say you could have at most 65ish years of programming since formal use in college.

No, it was not software engineering at the time per se but I'd absolutely call it programming.