Assuming you haven't tried anything to debug this (because otherwise you would have mentioned it, right? right?) here's the basics:
- Does the ESP32-C3 get power at all? Check your rails.
- Does the ESP32-C3 get taken out of reset? Check the EN pin.
- Does the ESP32-C3 get a clock signal? Use a scope to see if the 40MHz clock is oscillating.
- Do you get any sign of life on U0TXD? Normally you should at least see a signon message there.
In general, your schematic is not optimal, by the way: even if you get this working, you may have issues with reception because you haven't decoupled the power supply properly. Also, you probably want to remove C2. In general, I'd suggest you give the
hardware design guidelines for that chip a good read-through, it may mention other issues.