Glide-mirror symmetry in nonsymmorphic crystals can foster the emergence of novel hourglass nodal loop states. Here, we present spectroscopic signatures from angle-resolved photoemission of a predicted topological hourglass semimetal phase in Nb₃SiTe₆. Linear band crossings are observed at the zone boundary of Nb₃SiTe₆, which could be the origin of the nontrivial Berry phase and are consistent with a predicted glide quantum spin Hall effect; such linear band crossings connect to form a nodal loop. Furthermore, the saddle-like Fermi surface of Nb₃SiTe₆ observed in our results helps unveil linear band crossings that could be missed. In situ alkali-metal doping of Nb₃SiTe₆ also facilitated the observation of other band crossings and parabolic bands at the zone center correlated with accidental nodal loop states. Overall, our results complete the system's band structure, help explain prior Hall measurements, and suggest the existence of a nodal loop at the zone center of Nb₃SiTe₆.