Hi! Thanks for the feedback!
The game does start you within a certain distance of key resources, but somewhat farther than your suggested 6 tiles. The maps are varied enough that some of them simply don't have a start like that! (I'd like to avoid softening up the map generation too much because the variety in maps, including the challenge of dealing with occasional difficult resources, is part of what keeps me having fun...)
You're guaranteed to start quite close to science. And the game even tries to give the human player the best spot it found. So you can at least be fairly confident the AI had to work hard or get lucky as well.
All that said, you're right that it can still be frustrating, of course, and sometimes the logic above is not perfect! I think a lot of the frustration comes from starting off exploring in a bad direction, which is just random bad luck.
I recommend using the "show more start resources" option when you play custom games. It's on by default in other modes. It seriously reduces frustration for me, and gives me some good options for starting directions. Beyond that, I find that using science to find what you're missing as early as you can also helps a lot!
[EDIT: Woops, I forgot I had already released the improvements I mentioned, so I rewrote the above a bit.]