How could've the establishment of the Order in the region be prevented, and when would've been the latest for it ?
Quick response without too much thought:
IIRC (and that is a big assumption) OTL went something like
1200 Sword Brothers established in Riga
1225 Teutonic Order booted from Hungary. Invited by Masovia to come to Prussia.
1230's Lithuanians et al defeat Sword Brothers at Battle of Saul(?). Remaining Sword Brothers absorbed by Teutonic Order. TO goes on to dominate area.
I think the expelling of the Teutonic Knights is a critical point. If they never come to Prussia, the defeat of the Sword Brothers would at least temporarily remove the Orders from the region.
If there are still enough Old Prussians around in the 1430s (?), they could benefit from the Polish-Teutonic War. I am not sure if there were enough left at this point to resist assimilation.
Who will come to dominate the region in the absence of the Crusader Orders ? I assume it will be the Danes, but as whether it will be on the scale of OTL Teutonic Order in as immediately or not, I have no idea
My guess is that no one would dominate the entire region as quickly. The Danes would certainly be strong. Novogorod/Pskov could be more influential (this is the time of Nevsky). Swedes and Poles have a chance too.
If there is a great victory against the Orders, driving them out of the area, could it serve as rallying point for the consolidation of some of the Baltic peoples?