Brandenburg has no chance at unifying Germany without becoming Prussia. The other secular electors are probably the best bet. What about the Palatinate holds on Bohemia in the 30 years war. Bohemia and the Palatinate together is very strong
Why that? IIRC Brandenburg-Prussia became so mighty because of its military-focused leaders and the bulk of the army came from Brandenburg. Even with-out Prussia Brandenburg might do pretty well. Should they get Mecklenburg or some other area they might be able to pull off the unification like they did OTL.
But my strongest bet if not (Brandenburg-)Prussia, Austria or Bavaria is Saxony. Saxony was richer and more populous than Brandenburg-Prussia in OTL.
If we avoid the split of the House Wettin into Ernestines and Albertines and the resulting conflicts we might see a even mightier Saxony.
Instead of Augustus the Strong this Saxont gets a an Elector more focused on the army.
In the long run they could first beat Brandenburg-Prussia and take a part of the Brandenburg aswell as the Franconian holdings of the House of Hohenzollern, later they expand towatds the north, grabing some of the Saxons ancient homeland and gaining a sea-port. Later they beat Austria and unite the rest of Germany ... voila.
Interessting would also be the Palatinatian Line of the House of Wittelsbach. The start of the Thirty-Years-War plays out differently, the Winterking stays on Bohemia's throne. Austria is weakened, the Bavarians accept that the Wittelsbach of Bohemia-Palatinate are now the top-dog of the family and because of the quicker war less people die.
France has troubles of some sort, the Wittelsbach seize the opportunity and take Lorraine. The Imperial authority is meanwhile still weak and some weakling "rules" from Vienna. The Wittelsbach strike again and force the Eclestial Electors into becoming protectorates. The Habsburgs impolde finally and in the following succession war the Wittelsbach grab all their Burgundian holdings. They beat the French one more time (because why not) and create the Kingdom of Burgundy. Soon thereafter they are crowned Emperor.
In theory you could take nearly every dynasty/country and give them the favor of the doubt, with a POD around the Reformation nearly everyone could unify Germany.
Prussia had no extraordinal conditions. They had good rulers, good timing and good luck.