As Graydon Hoare notes in the comments on GitHub this wasn't the first repo so the real history goes back even further. He's also shared a "prehistory" repo [1] which is interesting to browse. The first commit [2] in _that_ repo is from 2008 but Graydon mentions starting work back in 2006.
Anyway in a sense this repo represents Rust in the real world rather than in gestation, so seems apt to call it the birthday.
[1] https://github.com/graydon/rust-prehistory
[2] https://github.com/graydon/rust-prehistory/commit/1969e085e3...
