Vim diff opens 2 files for diffing, but it doesn't navigate to the first diff section automatically on startup. Can I add something to startup script (like _vimrc) to do this?
]c doesn't jump to the first difference, it jumps to the next difference. If your first difference is on the first line,
]c would jump to the the second one which is not what you want. One could work around that with
]c[c (jump to next difference then jump to previous).
$ vim -d -c 'norm ]c[c' filea fileb
seems to do what you want.
I don't think it is necessarily a good idea to put that in your startup sciript.