What do you mean by recover? Brandenberg-Prussia didn't really take a leading role during the Thirty Years' War, though fighting did often take place in/near it. The war is usually broken into four phases defined by the leading opponents of the Habsburgs at the time: Bohemian, Danish, Swedish, French. Brandenberg-Prussia, as a protestant state, was allied against the Habsburgs, but never really took a leading role.

As for a little history about B-P. The crowns (and states) of Brandenberg and Prussia were joined in 1618 (they were both led by the Hohenzollren family). At the Peace of Westphalia (1648), Prussia won some territory, namely portions of Pomerania, which increased its prestige and made it the most powerful state in northern Germany and probably the second strongest German state overall (behind Austria, ahead of states like Saxony and Bavaria, though this is clearly subjective).

Now, we have to examine Prussia between the 1640s and 1701 when it became a kingdom. Really, it is important to go beyond just 1701 because this is more an examination of Prussia's rise to prominence in Europe as a great power. The most important Prussian rulers in this time are Frederick William the Great Elector (1640-88), Duke/King Frederick III/I (1688-1713), King Frederick William I the Soldier King (1713-40), and King Frederick II the Great (1740-86).

You're most interested in Frederick William the Great Elector, who strengthened Prussia allowing it to become a Kingdom. In the realm of foreign affairs, he cooperated with France to gain funds to rebuild his territories and armed forces after the 30 years's war. Additionally, he was able to win enough battles with Sweden to knock of the Swedish vassalage of Prussia, making Prussia only a "vassal" of the HRE.

Militarily, he was very successful, winning battles against Sweden (namely at Fehrbellin and during the Great Sleigh Drive) that helped end Swedish hegemony over north Europe. He also laid the foundation of Prussia/German military doctrines (Auftragstaktik = Mission-type Tactics) that were further developed by his successors that eventually led to Prussia military dominance.

In the domestic front, he grew the army to 40,000 (large for a non-Austrian German state). Also, after the revocation Edict of Nantes in France, he invited French Huguenots to Prussia, which helped develop the Prussia economic, technological, and pre-industrial base. He also invested in infrastructure, reformed state institutions, and reformed economic policies (taxes, tariffs, subsidies, etc.).

All these reforms, along with the slow expansion of Prussian territory, led to the growing strength of Prussia under Frederick William, which eventually allowed it to become a Kingdom during his son's reign.

I encourage looking more into the other rulers I mentioned earlier because their successful rule continued to empower Prussia and laid the foundations for it to unify Germany in the 1800s.