Rather than using a Vector or Tuple, this is exactly what CartesianIndex is for. Check this blog post for more info.
julia> x = reshape(1:27,3,3,3);
julia> getindex(x,(2,2,2)...) # splat a tuple
14
julia> getindex(x,CartesianIndex(2,2,2))
14
You can construct a CartesianIndex from a sequence of integers, a tuple of integers, or from various iteration utilities such as eachindex(IndexCartesian(),x), which returns an efficient iterator to produce the CartesianIndexes to access every element of x.
But as the above poster mentioned, you’ll need to tell us where these indices are coming from for us to really help you solve your problem.