I did not get into Homeland because of Claire Danes. I binge watched the entire first season in like three days (including skipping classes so I could finish the last two episodes of season one #oop) right as season two was starting because I was curious about it after it won all those Emmys in 2012.
(Quick aside for more Sara/Homeland origin story: I remember this week well, because it was right after midterms so I had a TON of free time… I also had just moved into a new apartment and had three free months of Showtime via my cable provider so I was like, “hey why not!?” I remember watching the last scene of the pilot where Brody is running and stops in front of the US Capitol and being like “fuuuuuuuuck…. well there goes my day.” If only I’d known the rabbit hole I was about to go down…)
After I was caught up and started watching live, week-to-week (“State of Independence” was the first episode I ever watched live and as a result I have a major sweet spot for it purely for nostalgia reasons), I began to consume everything about the show and Claire Danes, who was (and still is, duh) my favorite part of it.
I very quickly understood that I needed to watch MSCL and I finished my first run through of the series in December of 2012, during my winter break. I loved it (obviously).
I added several not-so-subtle hints in this answer to let you know that this all was happening when I was in college, which meant I was not watching MSCL when it first aired in 1994 on account of being a tiny child.