Sure, every well managed HOL-gladiator will touch BG anyway. Without any challenges, tricks and so on. Sometimes it may be even the gladiator which is "out of management"
You know, the Blood Gods bracket contains most "unfriendly" environment in the game.
Also, it contains other rules of the game. Which allows only 2 (3 if in Blood Games) fights per day.
So, I have the question : For what You need to do it as soon as possible?
The last of my gladiators which was climbed into BG was Tas To. He is retired now -- it was just the test run for Shadows...
He was sitting in the middle of Primus and he started to go up only when i pumped up Shadow Form for him. Faster and faster...
Please, use Your time in the Primus to "feel" the skills/strategies. Without such experience nothing to do in the BG.