Step 4 of 9 of the Sinnoh Throwback Challenge requires you catch a Ground-type Pokemon. Hippopotas and Gible are the only Ground-type Pokemon from the Sinnoh region that are wild spawns but neither has increased spawns during the event. Gible is available in 7km eggs and Hippowdon is a T4 raid boss. There are no Field Research tasks which reward a Ground-type Pokemon.
For people who cannot go outside to play this seems like a huge oversight. Even for those that can get out to play, I don’t know if Hippowdon can be solo’d so your best option is to find a Ground-type Rocket battle.