Well, what does construct provide to be able to do this? Maybe:
System: pick 3dshape overlapping point (mouse.x, mouse.y)
If the bottom of the 3dshape is on the z=0 plane then that will let you click on the bottom face. The other faces though? you're out of luck with Construct features. You'll have to do something from scratch...
First you'll need the mouse ray. You can get that from the camera distance to the screen. One way to calculate that is from a non scrolling 2d layer: xyz: (mouse("2d").x-320, 240-mouse("2d").y, 240/tan(fov/2)). 320,240 is half the viewport size. Next you'll have to normalize that vector and rotate it by the inverse of the 3d camera orientation. That will give you a ray direction from the camera position.
The second part is to do some kind of raycasting to see if and where the ray hits a 3d shape. Using an sdf with raymarching is a relatively simple solution for a single unrotated cube.
dropbox.com/scl/fi/on24os5ezt8bqkugnea58/raycast_mouse_cube.c3p
Overall for this kind of problem you figure out how to solve it from scratch and then adapt it to what features construct provides.