In my personal observation, mysticism is a function of the human psyche with a natural explanation and scientific evidence to support it. It is far stronger in some people than in others. I believe that for those in whom it is not very strong, but rather quite weak, it comes across as Divine Intervention when and if it is experienced. I believe that such experiences convince them absolutely of God’s existence and make such statements as, “I’ve experienced things that could never have happened if there were no God.” They are unable to describe the experience but in talking with and listening to a great many individuals over my lifetime I conclude that many have a once-in-a-lifetime mystical experience, or none at all.
I personally can bring it on pretty much at will. I’ve seen and heard other atheists whom I believe are similar, or who at the very least have some level of mystical experiences with enough frequency for it to feel familiar and common. So yes, it is possible for atheists to be mystics. The focus tends to be beauty, especially beauty of sight and sound, contemplation of nature, the universe, and deep space. Perhaps that is why we have so many atheist scientists, and also atheist artists, writers, poets, musicians and actors.