I know just a week or so ago on my "new" Feddie engineer, I was able to do diplomatic missions. I remember distinctly I was able to do a mission on Vulcan where I had to uncover a plot to assassinate a Romulan ambassador. I believe it was called Ancestral Sin.
I also see that I'm supposed to achieve the rank of Attache once I reach 160 diplomatic exp.
I started a science officer, hellbent on leveling only in explorations and diplomatic missions, the "Federation" way. Well, that Science officer is now level 12 and I just hit 170 diplomatic points.
And I have nothing. No Attache rank, no diplomatic missions..
Someone in-game told me I now needed 2,500 diplomatic exp? That's insane..It took me a week to get 170..
Do Doff Missions. I do not know what level you get Duty officers but when you do the diplomatic missions give you 50-300 diplomatic XP a mission. It still takes a while but it is much faster then doing diplo and aid mission alone.