Drinking beetroot juice that doesn't have nitrate in it every day for 12 weeks doesn't change the levels of nitrate or nitrite in your blood — so if you do see changes with regular beetroot juice, it's because of the nitrate, not the beetroot itself.
According to GRADE and EBM methodology, here is what ideal scientific evidence would look like to definitively prove or disprove this specific claim, ordered from strongest to weakest evidence.