If we count Macek-red (heavily edited stuff for US audiences), Star Blazers probably although it may have been Battle of the Planets.
If we count original stuff, we had a Japanese animation club (no, we didn't know in 1988 to call it "anime") at my junior high school, and the first thing I remember seeing there was the Macross movie (Do You Remember Love.) I'd already seen the US version of Robotech. I also saw Akira and Overfiend when I was in high school, and I saw the first Ghost in the Shell movie in the first US run at a showing at my college.
I didn't watch much anime until I started a job in 2006 with a lot of coworkers who were big anime fans (I went to see Girl Who Leapt Through Time on its early US run), and even there it took me more than a few years to really start catching up. AOT Season 1 was probably the first "big" series I saw as it aired vs. catching up after the fact.