The Mountain Underground Facility Key in Code Vein 2 isn’t accessible until quite a while after you’ve come across the door it opens. You find the door while exploring with Josee for the quest where you’re searching for the key to unsealing her cocoon.
Despite that, you can’t actually get the Mountain Underground Facility Key until you’ve completed Josee’s arc and can find her at the MagMell research building in the past, which is the same location you’d find Valentin.
Prerequisites for the Key
First, you need to finish Josee’s arc. This is absolutely required. Then, continue through and complete Lyle and Holly’s arcs as well, since you need Holly’s cocoon gone so you can reach a needed item.

After that, you can speak with Josee at the MagMell research building, where she wants you to gather some spices for her. This seems unrelated, but it’s the start of the side quest that leads to the Mountain Underground Facility Key.
Getting the Mountain Underground Key
When Josee asks for spices, you’ll find that the three she wants are located in areas that mimic the zones of the first three heroes.

First, you’ll find a Rich Spice to the northeast of the Sunken Pylon. It’s in one of the building ruins and appears as a glowing golden light rather than blue. You’ll come across it near the top of the building.

Second, you’ll find an Aromatic Spice in the Corroded Scar area. If you head to the Miners’ Abandoned Village and continue along the path to the northwest, you’ll come across the Northern Watch Fort. The spice is inside that building by some stairs.

The last spice is a Hot Spice, and it’s found in the Withered Greenhouse where you found Holly’s cocoon. Without the cocoon there, you can move around the greenhouse to find the spice.
Return to Josee with the spices and prepare for multiple cutscenes. After these, Josee will partner with you again and have a new request to visit the Mountain Underground Facility. This time, you’ll be able to open the locked door with Josee present in Code Vein 2.

