To unlock new teams, complete the corresponding objectives:

Auricom Team: Complete Franco Gonzalez Challenge with a Gold Medal.
EG-r Team: Complete Alex Reece Challenge with a Gold Medal.
Tigron Team: Complete Sveta Kirovski Challenge with a Gold Medal.
Xios Team: Complete Zala Woolf Challenge with a Gold Medal.
Pirahna Team: Complete Jann Shlaudecker Challenge with a Gold Medal.