You can drink green tea if you like, but it is gonna be harder to get the optimal amount of EGCG this way.
Here are some mean values of EGCG from various teas
Water temperature and brewing time will effect these values, but not by much. Your best bet is to supplement with EGCG and drink tea for leisure.
How your post reads suggest you believe natural > synthetic. This is not true. For EGCG, supplementating with EGCG is going to be more efficient then trying to get equal EGCG amounts from brewing tea.