Cycling through the faces may be a simple solution, but what is the problem you are trying to solve?
Clicking can cycle through all possible faces under the cursor, or if clicking needs to also deselect a face, Alt+Clicking or Option+Clicking can do the cycling. This does have some issues if the objects are more complex than cubes or if there can be many shapes stacked up in a scene.
What is the use case for selecting these faces?
If the objects really are transparent wireframes, there is no point of reference for what is the front or back of the object. You shouldn't treat faces that are towards the user differently if they can't tell which ones those are.
I can't think of a 3D modeling program that doesn't allow the rotation of objects or the camera. Users will likely expect this functionality, and with it the ability to turn things until they see what they want to interact with.
Most 3D modeling tools also offer alternative ways to select objects to deal with common scenarios that make visual selection of faces impossible. Consider a case with faces that are perpendicular to the camera (or nearly so): there may not be enough pixels on the screen to make a suitable click target. Or, what if there are 1,000 objects nested inside each other: any interface that works for 6 faces probably won't scale to 6,000.
Often these tools have a textual list of objects (and/or faces, edges, or vertices) that allows users to indirectly select the element they want to work with in situations where direct selection would be problematic.