Gundam: The Battle Master is the first game in the series, released for the PlayStation in 1997. Even this first game features the large multi-jointed sprites and 2-screen-high stages that the rest of the series would follow on. It includes the following mobile suits from the Universal Century era:

Playable

FA-010S Full Armor Enhanced ZZ Gundam
MS-06F Zaku II
MSM-03C Hygogg
MSN-02 Zeong
MSN-04 Sazabi
NZ-000 Quin Mantha
PMX-003 The O
RX-78-2 Gundam
RX-78GP02A Gundam Physallis
RX-93 Nu Gundam
Bosses (Non-Playable)

MA-08 Big Zam
AMX-002 (AMA-X2) Neue Ziel
Psyco Gundam Mark III
Hydra Gundam