As discussed in a previous thread, in an eventual alt-scenario where the Kingdom of Germany (based on the former East Francia) does not get involved in the Italian affairs and the Holy Roman Empire is not revived/created, it makes difficult that the Kingdom could become later a legitimate Empire without the Roman investiture.
So well, let's explore a different option: the Kingdom of Germany avoids any involvement in Italy (maybe France could do it instead?) and got focused on its expansion to the East (Pomerania, Prussia, the Baltic etc.) and maybe also to the Danube valley. Let's also assume that the formal Schism East vs West of 1054 is skipped and the Crusades do not happen as IOTL (something that could happen if the Papacy is more politically isolated, as ITTL there is no HRE and such).
Then, by the 12-13th centuries, Byzantium is getting gradually occupied by an alt-Turkic Empire and seeks help from the West (but no Crusades to Jerusalem etc. just help against the Turkic advances in the Balkan-Aegean area). The Kingdom of Germany is eventually getting involved (as the main military power in the West/Central Europe) but Constantinople finally falls to the Turks at some point (maybe earlier than IOTL).
As the sole Roman Empire has disappeared, now Germany (or any other country) could adopt the title of 'Empire' in the same way Russia did it IOTL (by claiming inheritance of the symbol/spirit of the defunct Roman/Byzantine Empire) and I don't think the Pope could avoid it at this point (specially when no Roman title had been ever restored in the West). There is also the possibility that the last Byzantine Empire could grant it to the King of Germany in the same way he did IOTL to the Kings of Spain, even if they never used it as it was already void.
So well, let's explore a different option: the Kingdom of Germany avoids any involvement in Italy (maybe France could do it instead?) and got focused on its expansion to the East (Pomerania, Prussia, the Baltic etc.) and maybe also to the Danube valley. Let's also assume that the formal Schism East vs West of 1054 is skipped and the Crusades do not happen as IOTL (something that could happen if the Papacy is more politically isolated, as ITTL there is no HRE and such).
Then, by the 12-13th centuries, Byzantium is getting gradually occupied by an alt-Turkic Empire and seeks help from the West (but no Crusades to Jerusalem etc. just help against the Turkic advances in the Balkan-Aegean area). The Kingdom of Germany is eventually getting involved (as the main military power in the West/Central Europe) but Constantinople finally falls to the Turks at some point (maybe earlier than IOTL).
As the sole Roman Empire has disappeared, now Germany (or any other country) could adopt the title of 'Empire' in the same way Russia did it IOTL (by claiming inheritance of the symbol/spirit of the defunct Roman/Byzantine Empire) and I don't think the Pope could avoid it at this point (specially when no Roman title had been ever restored in the West). There is also the possibility that the last Byzantine Empire could grant it to the King of Germany in the same way he did IOTL to the Kings of Spain, even if they never used it as it was already void.