You don't need the Empire's approval. Go with the merchants. Go with smaller ships. People seem to get so hooked on the. Treasure Ships they forget that China had other ships. Or just butterfly Neo Confucianism
Assuming for discussion's sake the state doesn't stomp down hard on overseas commerce.
Why are Chinese merchants going to set up trading posts in Africa? What is in Africa that is worth the costs?
As for smaller ships: Again, from the standpoint of government (or merchants), why is this worth spending money on?
Speaking from either's POV: I'm not going to spend a non-trivial sum on something that isn't a better use - from some standpoint of my interests - of that sum than spending it on something else.
Money spent on the navy is money not available for the army, or other concerns. Money spent developing new and possibly unprofitable trade routes is possibly a dead loss.
From the European standpoint, the potential gains are fabulous, thus OTL Europeans betting on this being a good idea. Not the same from China.