I definitely thought of how insignificant we seem against the enormity of the universe, but on an emotional level, I feel something more exciting: How lucky we are to exist and how amazing it is that we have the intelligence to even recognize the enormity of the universe, let alone be able to build huge telescopes and put them into orbit to get a better look.
As an atheist who doesn't believe in an afterlife or souls or anything like that, I get a thrill from the concept that life just happened somehow and yet it became something so very special. And the idea that it has likely happened before, could be happening now and will most certainly happen again and again in the future, on other planets somewhere out there is even more thrilling.
Of course, I do need to mention that even though I'm an atheist with regards to the idea that a god specifically created human life and watches over us and all that BS, I do believe that there is probably higher forms of life beyond the universe. Like the universe is just an atom in a bigger universe or something like that. And watching this film, looking at those images of nebulas and stars and everything... The predominant thought in my mind was, "What IS all this stuff?" I don't want to use the word "Why", as in "Why is it here?", because I don't think why factors into it. Cause and effect certainly, but not a purpose. I think existence just... exists.
So for me, the feeling of insignificane doesn't cause depression. It causes more wonder. It causes excitement about how lucky we are to exist and be as sentient as we are. That actually, in my opinion, makes life feel more valuable. Because if there's an afterlife, then what's so special about this life? It's just a test to see if we're fit for heaven or hell? After this, we either gotta spend eternity with God (who sounds like a judgmental, jealous and petty being) or burn in hell? THAT'S what would be depressing to me.
And I used to be such a nice guy.