A few years ago I was completing the IATA Diploma in SMS when I asked our esteemed lecturer what was the common road within industry to becoming a part of the safety management team at an airline. I asked this question thinking the safety manager was a specific career stream where one would go and do a selection of the courses listed in this thread, throw in a bit of flying experience, and climb the greasy pole.
In other words, train to be a safety professional!
My lecturer advised me that in his extensive consulting experience - over 3/4 of all 'safety managers' were airline captains or flight engineers that had failed their medical and had been put to work in the safety department. If their airline paid for them to complete a 2 week safety related course then that was a bonus.
I believe that there will be a lot of resistance in most airlines in allowing anyone to become a senior safety manager, regardless of your qualifications, unless you have been a Captain in that airline or have experience as a Captain somewhere else. In this industry, 4 bars still has more weight then a PhD when it comes to senior positions in any flight operations related capacity.
Of course if you want to be the COO, recognising the front of an aircraft from the back is purely optional.