Can the word "facing" be used both ways?

It's very common and perfectly correct to use facing in either "direction": problems can face us and we can face problems. At its core, facing is just a matter of orientation. If something has its "front" toward us, it is facing us. If we have our front toward something, we are facing it. When a problem faces us, it just means that the problem has presented itself to us. And it can do so whether we accept it or not: We can try to ignore (turn our back to) global warming, for example, but global warming would still be facing us, even as we avoid facing global warming.

Merriam-Webster has this to say about face:

6 a : to have as a prospect : be confronted by <face a grim future> b : to be a prospect or a source of concern for <the problems that face us> c : to bring face-to-face <he was faced with ruin>

The terms facing and faced by are somewhat interchangeable. If a challenge is facing you, it follows that it is also faced by you.