For this season, the best way is to unlock t4 for the other player via pits.
Then, you DON'T keep doing pits. You keep doing bosses (Urivar, Grig, Andariel, etc.) over and over. The lair bosses give you tons of exp.
Also, since they nerfed pit exp, this is also the reason for this method.
Leveling should take around 15 min.
As for the next season, it requires some more testing. The reason for that is that they nerfed the lair bosses' exp.
I may need to do more testing to see if the bosses are faster or pits is faster in season 12.
Just tested this methode:
T4 unlock with pit 60 new char @ lvl 14
first kill T4 varshan new char @ lvl 24
second kill varshan new char @ lvl 28
(Urivar is proberly a better choice because he give more xp)
Still if you are just a few days in a new season you chance is high:
- you cant do t4 bosses that is less xp t4 varshan give around 4 mil and t1 varshan 1 mil
- you dont have enough materials. And since you need to open the chest you have to leave dungeon and reset dungeons.
Did my new char leveling this season with azmodan normal runs. No hassle

running around a bit but most of the time afk and in about 1 to 1,5 hour leveling done.
Maybe new season will offer a simular methode if not bossing is the way to go.