What group pushed Germanic people into Roman territory?

The main group that pushed Germanic people into Roman territory was the Huns. As they expanded their empire in the 4th century, the Huns pressured various Germanic tribes, including the Visigoths and Vandals. This migration was driven by the Huns' aggressive military campaigns, which led to significant upheaval and displacement of these tribes, ultimately causing them to seek refuge within the borders of the Roman Empire.