It's worth starting at the beginning of the war for this. Prussia’s position at the beginning of the Seven Years’ War was a daunting prospect. Prussia was a diverse grouping of territories under one leader, with minimal unity between provinces. The state was well-defended to the south, but its east and west borders were somewhat vulnerable. Think of Silesia, somewhat isolated and connected to the rest of Prussia by a strip of land just a few miles wide (Simms, p.2). Of course Prussia was not unique in this regard – its main rival Austria possessed geographically diverse territories and weak borders to its south and east. But Prussia was also smaller in all aspects, with a fifth of the population of France, and a third of Austria’s. This showed in the following war, when Russia was more than willing to accept massive losses in order to secure victory, which Frederick could not afford (Scott, p.39). Of course, Prussia had some advantages, not least the formidable abilities of its monarch, Frederick II. Frederick also possessed combined political and military leadership, which his opponents did not enjoy. Nonetheless the outcome of the war went well beyond expectations, with Prussia securing a more stable position in the European balance of power and establishing the state as a great power in Europe.

The role of Britain was huge in ensuring Prussia's survival. Grant of £670,000 per annum were provided from 1758 to 1761 (Robson, p.472). As well as this, the British financed the Army of Observation under Prince Ferdinand of Brunwick, given £1,200,000 in 1758, used to protect Prussia’s Western front. Britain used its financial weight to subsidise Prussia’s armies and provided military experience. The alliance was of course an act of sheer political expediency; the aim for Britain was to draw French resources towards continental commitments in order to distract it from what Britain saw as the real struggle: mastery of the colonies and the seas.

But even with British subsidies, the strain on Prussia began to show as the war progressed. You've already mentioned the "Miracle of the House of Brandenburg", so there's no need to go into detail on how close Prussia was to defeat in military terms. But in 1759 Frederick mustered only 100,000 men, the same in 1760, compared with 143,000 in 1756 (Scott, p.35). By the end of 1761, Prussia was on the brink of financial collapse. Of course, much the same could be said for Austria, whose state finances were similarly dire. However Prussia also had to manage with the Austrians and Russians taking swathes of Prussian territory, including Silesia and Western Saxony, and this denied Frederick desperately needed resources. In the words of the ruler himself:

“Every bundle of straw, every transport of recruits, every consignment of money, all that reaches me, is, or becomes a favour on the part of my enemies, or a proof of their negligence, for they could, as a matter of fact, take everything. Here in Silesia every fortress stands at the disposal of the enemy. Stettin, Cüstrin and Berlin itself are open to the Russians to deal with at their pleasure…” (Robson, p.478).

But the collapse of Prussia was not to be. The death of Elizabeth of Russia in early 1762 took away the main aggressor against Prussia. The Tsarina was replaced by the far more compliant Tsar Peter III, who abandoned the Austrian alliance and made peace with Frederick. Peter III was soon assassinated, but his successor Catherine II was not interested in continued war. Austria, now isolated in its opposition to Prussia, could not defeat her singlehandedly. Prussia, through the fortunate death of the Tsarina and the following reversal of Russian policy, was saved.

Quite incredibly, Frederick did not come out of the war entirely broke, quite unlike Austria. Hohenzollern policy for some time had been to hold a reserve of cash “for strategic purposes”. In 1763, Frederick therefore still held a reserve of over 14.5 million thalers (Scott, p.42). But Prussia was certainly not in a position of financial health, as not only was this reserve effectively an emergency fund; this small amount of wealth also ignores serious financial, demographic, and economic shortcomings.

Table below: Rights to new livestock and repairs required in 1763-4, following the war (Robson, p.485):

---	Livestock	Houses	Barns	Stables
Pomerania:	8766 (a)	1246	-	-
East Brandenburg:	68,666 (sheep only)	(b)	-	-
Silesia (open country):	-	3723	2225	3495
Silesia (towns):	-	2917	399	1380
The Electoral Mark:	218900 (c)	-	-	-

(a): Cost totalling over 200,000 thalers. (b): Towns such as Cüstrin were entirely destroyed by bombardment. (c): Total of 25,000 horses, 17,000 bullocks, 20,900 cows, 121,000 sheep, and 35,000 pigs.

Industries such as the Silesian linen industry were decimated by the war. The linen industry only fully recovered by 1784. In terms of demographics, one out of nine people in Prussia had died during the war, a massive 500,000 out of a population of 4,500,000. Frederick himself certainly understood the dire situation the Prussian economy was in following the war, claiming:

"The nobility and the peasants had been pillaged and ransomed by so many armies that they had nothing left except the miserable rags which covered their nakedness. They had not credit enough to satisfy their daily needs. The towns no longer police. The spirit of fairness, and order had been replaced by anarchy and self-interest. The judges and the revenue authorities had given up their work owing to the frequency of invasions. absence of laws a spirit of recklessness and of rapacity arose. The nobility and the merchants, the farmers, the working man and the manufacturers had raised the price of their labour and products to the utmost. All seemed intent upon ruining each other by their exactions. That was the terrible spectacle which the formerly so flourishing provinces offered after the conclusion of the war" (Robson, p.484-5).

Frederick therefore focused heavily on rebuilding the economy and trade in order to restore his own finances. Taxes were imposed on luxury imports, to attempt to restore a balance of trade and stimulate domestic production. One major change made to Prussia’s financial system following the Seven Years’ War was a further shift towards heavier reliance on indirect taxation. Revenues from customs and excise duties rose between 1740 and 1786, from 35 per cent of tax revenue to 60 per cent (Schui, p.372-3). In particular this meant that towns bore a heavier tax burden. In 1766 in response to the financial situation created during the war and difficulties in raising taxes, Frederick created the Régie in 1766, a new administration aimed to extract more in taxes from Prussian towns. This included the drafting of French tax officials to replace Prussian tax farmers in order to create more efficient tax collection, which was hugely unpopular with the Prussian nobility.

Prussia’s financial and economic situation was remedied over time. The first Polish partition, 1772, helped restore the health of the Prussian state. West Prussia had much arable land, allowing Prussia to be able to export grain and be less prone to famines such as in the early 1770s (Dippel, p.201). In terms of trade it gave Prussia access to trade on the Vistula, addressing the trade imbalance. Through the creation of new industries, continued possession of Silesia, the acquisition of new territories in the partition, and the sponsorship of trade and the economy, Frederick was able to restore the state. At his death, over 50 million thalers were held in the treasury, compared to 10 million in 1740 and 14.5 million in 1763 (Dippel, p.213).

Compare the outcome of Prussia to some European rivals. Austria’s aims had been to recover Silesia and reduce Prussia to a minor power if not outright defeat it, as well as limiting Russia’s influence. These both failed. France as well had been solidly defeated in the battle for the seas and colonies. Its colonial possessions had been massively reduced, and its main rival Britain was victorious. French prestige had reached a new low, but we must not underestimate France’s continued potential. Remember that only a few decades later France conquered half of Europe, even if its military power had been destroyed temporarily (Scott, p.57). With a population of 25 million which only continued to grow, a strong agrarian economy and secure borders, France was not quite reduced to a second-rate power. Nonetheless, France's position was far weaker than in 1756, and Louis XV's prestige was badly damaged.

Prussia was certainly devastated by the end of the Seven Years' War, but not irreparably so. Frederick emerged in a far better position than Austria and France, who were the true 'losers' in the war, and through a number of factors as listed, was able to recover to a position as a first-rate power in Europe.

Sources:

Dippel, H.: ‘Prussia’s English Policy after the Seven Years’ War’, Central European History, Vol. 4, 3 (1971).

Robson, E.: ‘The Seven Years War’, in Lindsay, J.O. (ed.): The New Cambridge Modern History (1957).

Schui, F.: ‘Taxpayer Opposition and Fiscal Reform in Prussia, c.1766-1787’, The Historical Journal, Vol. 54, 2 (2011).

Scott, H.M.: The Emergence of the Eastern Powers, 1756-1775 (2009).

Simms, B.: The Struggle for Mastery in Germany, 1779-1850 (1998).