A good question is “with what rocket?”
Probably Yenisei which unfortunately had its development paused.
A factor in this crash is that they lack a round-the-world comm system.
They've had this with GLONASS for over a decade. For far-side communications, you need a single relay satellite like what China used for Chang’e-4. However, you don't actually need either of those for many lunar missions. When the Americans sent humans to the moon, they just used radio waves that were picked up from various ground stations across the world.
You've based your perception of China on fundamentally incorrect axioms, so there's no discussion to be had here. We can talk about radiation if you want.