Why would you need to use itertools.product() together with numba?
You do not report to have large dataset so do not seem to be needing the speedup.
If you use numba njit, in general working with numerical data only, e.g. numpy arrays or doing for loops, works best. If this is the case for you, replace the itertools solution with for instance a numpy solution.
However, since you use the itertools solution I am assuming you use python lists with non-numerical data. Since itertools is not supported, you could implement it yourself like for instance in this post, but is probably not required for what you want.
Long story short: do not try to compile itertools with numba njit when that is not necessarily required. I suspect just using itertools is your best shot.