I'm not seeing a timeline in your link above.
According to Wikipedia's Vulkan article [1], "The Khronos Group began a project to create a next generation graphics API in July 2014..."
Wikipedia's Metal article [2] links to the presentation from WWDC 2014 (the first week in June 2014) where Metal was introduced. Apple doesn't ever per-announce APIs-- at this time Metal was available for developers to use.
The Mantle article [3] says AMD developed Mantle "...starting in 2013" (the referenced Forbes article is from September 2013.) I'm doubting this was ample notice for Apple to have elected to write Metal, design it, and implement it nearly completely for June 2014. However, I'd concede it is certainly possible (Apple just doesn't seem that nimble to me.)
I'd be interested in reading anything more authoritative than a comment board on the impetus behind what seems to be an industry-wide decision to create these lower-level APIs.
1 - https://en.wikipedia.org/wiki/Vulkan_(API)#History
2 - https://en.wikipedia.org/wiki/Metal_(API)
3 - https://en.wikipedia.org/wiki/Mantle_(API)