The germanic peoples began moving towards the east, as part of a great migration and conquests. The historical beginnings of Prussia and Austria are quite interesting.
Prussia was essentially founded by the Teutonic knights, an order of germanic warrior monks who had early been established to fight in the Crusades.
The Austrian monarchs, through a long series of strategic marriage alliances managed to gain possessions all over Europe. The Austrian monarch was able to obtain the title of Holy Roman Emperor, a legacy of the confederation of states left behind by Charlemagne many centuries before.
In both cases, Austria and Prussia were described by contemporary historians as basically a military with a state, rather than the other way around. This likely had to do with the two states having historically been founded by conquest to begin with, so their political structures were fundamentally militarized. In both cases, the german language and culture was imposed as the dominant one. Both Austria and Prussia would go on to carve out empires out of a diverse group of peoples. Prussia consolidated its power in the east, encouraging more german migration, while "germanizing" the subjugated Baltic people, and was eventually able to unite the original german states. Austria reigned over a much more diverse empire, through an early political union with the kingdom of Hungary, though the union was never an equal one. This culminated in the German Empire and Austria-Hungary, which were defeated in the first World War. Both Empires created magnificent capitals, in Konigsberg and Vienna. The architectural marvels of Vienna still stand as a testament to Austria's Imperial past, while every last trace of the Prussian history of Konigsberg was intentionally obliterated by the Russian Soviet occupation after the second world war. During the time of Hitler there were still numerous magnificent Teutonic Castles and great Prussian monuments commemorating war victories. While Vienna had always been famous for hosting a diversity of different peoples in the empire, the city became much more homogenous after the fragmentation of the empire. Historically, it is really no surprise that Hitler wanted to annex Austria. It was a germanic state, and with Germany's Prussian origins, which were quite recent in fact, it was only obvious to want to reunite with the remnant of Prussia's sibling geramic empire. This was a time of Nationalist ideology, it should be remembered. While Nationalism had contributed to the unification of the german states, it was also the fundamental reason for the breakup of the Austrian Empire. In conclusion, the states of Austria and Prussia had many historical parallels, and both left behind an influential legacy in the existence of the modern political boundaries in central-eastern Europe.
It should be remembered that both Prussia and Austria were really part of a german migration and subjugation of Slavic peoples to the east. In both cases, there was a deliberate attempt to "germanize" the occupied slavic peoples, as their culture, language, and political institutions were believed to be inferior.