OK in the interest of science and not being a hater I have done what you asked for all minor league seasons from 2006-2016 - but I set the min PA to 150 (180 seemed like it was cherry picking too much) and included low and high a as well as the south atlantic (A), and I didn't control for position at all since hitting is really it's own skill independent of fielding ability. Each line is from just one season except for the final column which is career WAR (so there are 2 mike trouts). Players who played across multiple leagues in one year are also included so some players (like Jaun Soto) have a large amount of their numbers coming from rookie ball even though they played a bit in A ball.
bb% > 5%
K% < 20%
age < 22
wRC+ > 145 (set here to include Trout's age 17 season, and because as you increase this you start to run out of players really fast)
babip > .380
http://i.imgur.com/Q8x1L4k.png
Some interesting take-aways:
Bo's brother is on the list
Bo would have the 2nd highest wRC+ on this list (below Mike Zunino and above Oscar Taveras)
Bo's babip would be the highest on this list (just slightly above Myles Straw)
Just 17 out of 73 players are 0.5 career WAR or above. If you change the wRC+ to include only >180 then only 10 players remain on the list. JD and Mike Zunino are the only ones to have positive WAR. At first I was thinking I would hold my ground here, but....
Only Zunino's wRC+ is over 200. One guy. If Bo was hitting closer to a 170 or even 180 clip I would probably have been right about not getting hyped. But the reality is that there just hasn't been anyone, ever, to have done what Bichette is doing. Even if you regress his BABIP all the way to the mean (of this group of comparables) which is 0.404 - this removes about 6 hits - and even if we say those are all doubles his wRC+ only drops to around 200 from 205.
Conclusion: What Bo is doing is definitely historical - quite possibly the best performance in the history of A ball (assuming he doesn't go into a huge slump before his promotion). In general you shouldn't get excited about babip driven success - there are a lot of players on here who never amounted to anything - but Bo is by far the most successful of any of them. So yeah.. Get Hyped