Technically, immediately upon the death of Charlemagne in 814.
Although Carolus graduated from rex Francorum to being crowned Holy Roman Emperor in 800, the 'Empire' he founded was largely a personal one. Upon his death, his territory was split between his sons into the three provinces that would become Francia, Lotharingia and Germania. The Holy Roman Empire that we think of as a mainstay of the Medieval and Early Modern periods was actually a separate political entity, founded by Otto I of Germany in 962.
Son of Henry 'the Fowler', Duke of Saxony, Otto I became King of the Germans in 936. In a roughly similar trajectory to the earlier Charlemagne within Francia he spent the early part of his reign greatly strengthening royal control over the various provinces of Germania, centralising power to the crown from the nobility and using the Church as an arm of state while strengthening royal military power. Following his defeat of both Wendish and Magyar uprisings and invasions at the battles of Recknitz and Lechfeld in 955, the latter earning him great plaudits as a saviour of Christendom as Hungarian raids had been increasingly troublesome for some decades, Otto launched an aggressive programme of expansion into both Pagan Slav and Wendish territories and into Italy, capturing much of Italy by 961 and having himself crowned Holy Roman Emperor the following year. It is this Germanic state which then survives until the 1800s.