Long story short, I've read that some believe it's possible, but not easy. It requires cron, which isn't part of Solus. I was a TimeShift user in other distros, and was disappointed to learn that it's not here. But I found a backup solution that I like very much, and it is in the Solus repository.
It's called "restic," and if you search for that name in the forum, the first result you see will be a short tutorial that I wrote to introduce folks to it.
