After completing first two levels, Rude Awakening and N. Sanity Peak (plus a cut scene), you will be taken to the Dimensional Map. From here, hit
to pull up the Skins menu, and press
to swap to Coco.
Select any skin (besides the first one), and this should unlock.
If you pre-ordered the game, or have linked your Activision account, you should have these skins unlocked as the last ones.
If not, complete all of the gem missions in a level to unlock a skin for either Crash or Coco (40% wumpas, 60% wumpas, 80% wumpas, All Boxes, Minimal Deaths, and the Hidden Gem). The first two levels make this easily doable. The first level is easier for minimal deaths, but the hidden gem can be seen quite easily in the second.