It’s definitely possible! To tell whether you are speaking or singing through your nose, place a fingertip lightly under each nostril: if you can feel air coming out of your nose when you speak, or your nose feels like it’s vibrating, make a conscious effort to direct the air out through your mouth. Even if you don’t know exactly what muscles you’re using, your body will probably know what to do.
After a little bit of experiment myself, I can tell you that it’s near impossible to make a nasal sound when your mouth is open and tall like a 0. In singing, a ‘two-finger-gap” between your lips is ideal, but for this stick three fingers in your mouth (one on top of the other) and make an ah sound. You should notice that it’s much easier for the air to come through your mouth than through your nose. Then, try to recreate this feeling when speaking normally.