Through his mother, Flavia Sabina, a cousin of the Roman emperors Titus and Domitian, his connections enabled him to hold a series of civil and military imperial appointments.

[6] His senatorial career likely began in his teens as one of the tresviri aere argento auro flando feriundo, the most prestigious of the four boards comprising the vigintivirate.

"[8] Syme explains he earned these dona militaria from actions in Domitian's campaigns in Pannonia around 92, in response to the Sarmatians and Suebi having invaded that province and destroying Legio XXI Rapax.

Syme provides a possible solution to this puzzle: he notes that the governor of Cappadocia, Lucius Antistius Rusticus, died in office in AD 94; he proposes that on the death of Rusticus that the province was temporarily divided between the two legionary legates, with Sospes, legatus legionis or commander of Legio XIII Gemina, assuming control of Galatia and the neighboring districts, while the other assumed responsibility for the parts of Cappadocia bordering Armenia and Parthia.

Syme speculates that this achievement was "not unalloyed bliss": Lucius Caesennius Sospes held the fasces the same year that Trajan marched into Armenia, and the first place he occupied was Arsamosata, where his father had surrendered to the Parthians in AD 62.