Yes! Thank you both for your help. Upon further review and confirmed by my dh, Chinese Privet (Ligustrum sinense).
So I'm aborting my mission to propagate.
But, on the good side, I'm going to look into finding an Osmanthus somewhere on line to purchase. So, I'm very happy
@Silversurfer that you considered it. Thank you.
I'm going to consider this solved as Ligustrum sinense.