I don't think so. If that was the case, then for any program we could compute its length n, and then ask the all-knowing oracle the value of BB(n). And knowing

I don't think so. If that was the case, then for any program we could compute its length n, and then ask the all-knowing oracle the value of BB(n). And knowing BB(n) for any n we could solve the Halting Problem, but we know that the Halting Problem is unsolvable. Therefore we must conclude that such an all-knowing oracle can't exist.