As always with the history of continental Europe it's all Charlemagne's fault.

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When you say "At the time", I assume you mean in 1871? This is a tricky question to answer because while "Germany" as a national entity was a new player on the stage of major european powers, Germany as an ethno-cultural (for lack of a better term) entity was not. The German Empire was new in name but old in the game as it was, for the purpose of its role as an international player, really just Prussia+. The German people had for a since the dissolution of the HRE been two major players, Prussia and the Austro-Hungarian Empire. The history of the two German empires is long and interesting but let's skip 98% of it an jump in about 55 years earlier, just after the fall of Napoleon.

At this stage the major European players basically said "Enough of this revolutionary nonsense! Shit's scary and we want things to be as they always were!". In Austria, Klemens Wenzel Nepomuk Lothar, Prince von Metternich-Winneburg zu Beilstein (or just Klemes von Mtternich for short) called the diplomats and statesmen of Europe together to say, in a lot more words, what I started this section with. They all agreed that Europe needed more "legitimate rulers" who showed solidarity to one another against the revolutionary threat. This was unsurprising since they were all called Von This, Lord that or Earl of BFE and all represented men who like titles like King, Queen and Emperor and really didn't like things like revolutions and nationalism.

In Vienna von Metternich managed to get them all to agree that shutting down ideas like equal rights and liberalism was very important and that legitimate rulers should stick up for one another to do just that. They agreed to a whole lot of things but here we'll focus on Germany. Germany was reorganized into a loose conferedation of free states (39) and cities (4) not entirely unlike the HRE and under Austrian leadership. A few years later an angry liberal student murdered a conservative playwright called August von Kotzebue, he was more or less the Tomi Lahren of his day. In response the Carlsbad Decrees were signed which suppressed liberal student unions, restricted freedom of the press and threw a lot of liberal professors out of the universities. Not a whole lot happened for a bit except the founding of the Zollverein (customs union) which included the German states except Austria, this was basically an early indication that there was a growing need for administrative and economic unity spurred by the industrialization of the German states.

Fast forward to 1848. Revolutions! Again! Curses! It all began in France, again, and when Louis-Philippe abdicated and went into exile in Britain they spread throughout Europe, mainly to Germany. Generally there were two factions, the workers who were early socialists and wanted radical improvents to their quality of life and the middle classes who were liberals and wanted radical improvement to freedom of speech, assembly, press and so on. I will not go into the giant clusterfuck of loosely coordinated revolutions that took place in the German states but here's what happened. The revolutionaries met with early success, in Prussia King Friedrich Wilhelm IV promised improvements and the revolutionaries were hopeful. They formed a national congress, discussed a bunch of things and offered Friedrich Wilhelm the Imperial Crown under a new constitution. However, while that happened the "old guard" (mostly princes of local states) had rallied, mobilized the army and retaken control. As soon as Berlin was recaptured Friedrich declined the crown, ostensibly because he could not take it without the consent of his peers but privately he wrote that he was insulted at being offered a "Crown from the mud". The March Revolution was a failure.

Queue another period of repression, limited freedoms and absolute monarchy until 1857 when Friedrich Wilhelm IV has a stroke and Wiliam I becomes King of Prussia. He recruited some really good people. Namely Otto von Bismarck (Chancellor) and Helmut von Moltke (the elder, his nephew with the same name commanded the German army at the outbreak of WWI). This trio (along with Albrecht von Roon, defense minister) would go on to unify Germany. I will cut this down something fierce but basically Bismarck was brilliant in maintaining public order, furthering industrialization and improving the daily life of many Germany and von Moltke is someone I regard as one of the great military geniuses of history who reorganized the German/Prussian army.

There was a brief war with Denmark over who should have Schleswig and Holstein, 39 German states, 4 free cities and the Austro-Hungarian Empire vs Denmark. Needless to say Denmark was a little out-gunned. Now, thus far Austria was in agreement with Prussia in so far as that Schleswig and Holstein were German lands but, they wanted to establish two new free states whereas Prussia wanted to annex them. So, Prussia went to war with Austria. The brand new Prussian Army met the old Austrian army in Bohemia. It did not go well for Austria. However, Bismarck was very nice in the following peace settlement and wars between the two was nothing new so they remained on relatively good terms.

After what became known as the Seven Week War the German Confederation was officially dissolved and the North German Federation was formed. It may have been a Federation in name but in reality it was Germany under Prussian rule. It was a transitional period that eneded in 1871 when the German Empire was formed.

But... what about my question? Was it perceived as a threat to European Stability?

Well, it depends on who you ask. If you were France. Yeah. If you were British upperclass? No. Bismarck was very concerned with maintaining European stability, something the British really liked. They were also, at least initially, positive or at least neutral about German colonialism which they saw as a counter-weight to France(but I'm getting ahead of myself, this was later). Tsarist Russia too was initially positive about the German unification, especially during the period of the League of Three Emperors (Dreiskaiserbund).