Maybe this:
julia> vec_of_arr = fill(rand(3,4,5),6);
julia> arr = cat(vec_of_arr...,dims=4);
julia> size(arr)
(3, 4, 5, 6)
You can use permutedims(arr, (4,1,2,3)) to move the last axis to first position in indexing.
Check the documentation for cat and permutedims for more information.