Optimizing distance between surfaces calculations

I need to find the distance between an object and a very large mesh (65000 triangles). I have a loop to determine the distance between vertices using Vector3.Distance (these correspond to vertex colors on the object, creating a distance map). It works, but Unity crashes when I do it for the large mesh (too many calculations).

What are ways I can optimize so I do not have to go through each vertex but can maintain the integrity of an object with a complex shape ? Would appreciate any direction in how to do this computationally/sort through the mesh for relative distances, euclidean path,etc?