I’m not sure what you mean by “not officially engaged”. Does that mean you have decided to marry one another but don’t have a ring? Or, you’ve casually talked about maybe getting married someday?
I think it makes a difference- if you’re engaged but with no ring, you’re still engaged. In that case, there’s no reason not to start pre-Cana.
On the other hand, some marriage prep programs involve discussion of some pretty intimate details- some physical, some emotional- that really might not be appropriate for a couple who isn’t sure they’re getting married yet. In that case, if you’ve only talked about getting married casually and haven’t actually planned to marry, I would wait. These programs are designed for people who have already decided to marry and know when. They will want to know when your wedding date is when you sign up, to make sure the church is free and the priest is available, and if you don’t know those things they may even ask you to come back when you do know, so that they can focus the program on the couples who are actually engaged.