We present initial results for post-processed GNSS orbit and clock estimation for the FORMOSAT-7/COSMIC-2 (Constellation Observing System for Meteorology, Ionosphere, and Climate) constellation. The six COSMIC-2 satellites launched on June 25, 2019 into a 24 deg inclination, ~725 km circular orbit. The primary Tri-GNSS Radio-occultation Receiver System (TGRS) payload tracks GPS and GLONASS signals on two upward looking precise orbit determination (POD) antennas. We evaluate three GPS and GPS+GLONASS POD solutions applied at the COSMIC Data Analysis and Archive Center using the Bernese GNSS Software. The obtained results are very consistent for the six satellites. Orbit precision estimates are below the 10 cm and 0.1 mm/s 3D position and velocity requirements, respectively. A test case applying carrier phase ambiguity resolution indicates this technique may support the generation of more precise orbits in the future.