On the contrary, from the 900s onwards, much of what we now consider Germany was in fact unified under the Ottonian Holy Roman Empire, founded largely by Henry the Fowler, Duke of Saxony, and his son Otto, who would be crowned Holy Roman Emperor Otto I in 962. This was the 'First Reich' which would underpin later ideas of German nationalism in the wake of Napoleon's dissolution of the Holy Roman Empire in the early nineteenth century. Although this was often disrupted by political upheaval, particularly during the minority of Otto III in the late tenth century, the HRE nonetheless remained territorially intact, and indeed aggressively expansionist into the high medieval period.

It's not my area of expertise so I can't explain in depth as to the political and religious upheavals which split the HRE apart in the late medieval and early modern period - events surrounding the Reformation and the 30 Years War - but certainly in the early medieval period, there was for all intents and purposes a unified Germany.