If I'm going to needle felt a design, I prefer to do it after the soap is fully felted so the design stays crisp and clear
If the soap is well cured and hard, I agree you won't be able to stab directly into the soap without a high risk of broken needles. If the soap is young, however, the soap can be soft enough to gently stab into. Maybe not forceful stabbing, but you're not having to needle felt more than 1/8" of fiber so force isn't really necessary.
Other tips -- Try stabbing sideways, rather than directly down, so the needle is passing only through the fiber, not into the soap. Pull the needle straight out on the same path that you stabbed the needle in. Don't twist or bend the needle as you work -- it doesn't take much to break a needle if you "put some English" on it. It's easy to break needles when I get tired, so I also take frequent breaks.