I had seen Iron Man and Iron Man 3 in 2013 but not really picked up on the MCU concept.
I was meeting a friend in Spring 2014 and we decided to go to the cinema. Not at all clued into any of this stuff and having not seen The Amazing Spider-Man or most of the Raimi trilogy, "that latest Spider-Man film" seemed like a safe bet (The Amazing Spider-Man 2). But we messed up the date and it wasn't on. The people at the cinema said "How about the latest Captain America?"
I didn't really want to, "Captain America, seriously? Isn't that like some weird American patriotic propaganda Superman-y silly character?"
My friend, who was a little more clued in on the MCU and had seen Captain America 1 and Avengers, encouraged me to give it a try, and if we didn't we'd have wasted going to the cinema, so I gave it a try.
And it was nothing like I expected, and I loved it (and obviously, it turns out I watched the way better film). And picked up on the MCU tie-ins, so asked my friend all about what that stuff was on the way back. Learned about the MCU, went home and spent hours online reading up about it all, and the connectivity aspect and timeline and watch order and everything completely captivated me and clicked with the way my brain works.
Watched them all over the following months and caught up with Agents of S.H.I.E.L.D., and then I was completely caught up and sucked in by late 2014/very early 2015. And the rest is history.