To make this happen i think the best bet would have been the revolution in 1848 --- IN 1849 the crown was offered to William of Prussia (Austria was in turmoil, as was the rest of Europe)
https://en.wikipedia.org/wiki/German_revolutions_of_1848–49
On April 2, 1849, a delegation of the National Assembly met with King Frederick William IV in Berlin and offered him the
crown of the Emperor under this new constitution.
Frederick William told the delegation that he felt honored but could only accept the crown with the consent of his peers, the other sovereign monarchs and free cities. But later, in a letter to a relative in England, he wrote that he felt deeply insulted by being offered a crown "from the gutter", "disgraced by the stink of revolution, defiled with dirt and mud."
IF Fredrick William HAD taken the crown -- and put pressure on Russia not to support Austria (given Russian some land) -- i think this would have happen --most likely
1. FW would accept the crown
2. Hapsberg family takes over kingship of Hungry (with out Russian help they would have been overthrown)
3. France and rest of Europe was in chaos
4. Germany (or HRE rebuilt)
5. The revolutionaries wanted a German only type country