My personal recommendation for a Tarkovsky's first is his diploma film The Steamroller and the Violin (1960, 46 min, co-written with Andrei Konchalovsky).
It was surprisingly watchable [for me] and I wish I had watched it first myself before I was exposed to the Mirror when I was 16.
[0] https://en.wikipedia.org/wiki/The_Steamroller_and_the_Violin