Why is it impossible?
The Church was a meritocracy in OTL.
The Papacy often attempted to, and almost achieved multiple times, gain supremacy over the various secular forces; nobles/emperor of HRE. You need only use one of numerous POD's.
"From the late 6th to the late 8th centuries there was a turning of the papacy to the West and its escape from subordination to the authority of the Byzantine emperors of Constantinople. This phase has sometimes incorrectly been credited to Pope Gregory I (who reigned from 590 to 604 A.D.), who, like his predecessors, represented to the people of the Roman world a church that was still identified with the empire. Unlike some of those predecessors, Gregory was compelled to face the collapse of imperial authority in northern Italy. As the leading civil official of the empire in Rome, it fell to him to take over the civil administration of the cities and to negotiate for the protection of Rome itself with the Lombard invaders threatening it. Another part of this phase occurred in the 8th century, after the rise of the new religion of Islam had weakened the Byzantine Empire and the Lombards had renewed their pressure in Italy. The popes finally sought support from the Frankish rulers of the West and received from the Frankish king Pepin The Short the first part of the Italian territories later known as the Papal States. With Pope Leo III's coronation of Charlemagne, first of the Carolingian emperors, the papacy also gained his protection."
https://en.wikipedia.org/wiki/Papal_supremacy#First_phase_of_papal_supremacy