The design looks OK and all the power rails look OK too.
Does the board power up if you connect to USB (preferrably via a current limited power supply and not actual USB port)? ie, does the 5V look OK when you do this? If 5V is OK, is 3.3V OK?
If both 5V and 3.3V are OK on the USB supply input, then the fault lies in the MIC area. Diode D2 will cause a failure of the power supply if the wrong way around. Double check all capacitor polarity too. The line on these SMD represents the pos terminal, unlike the electrolytic types where it marks the NEG terminal. I’ve seen some PCB houses put these the wrong way around too.
If there is no 5V when powered on the USB side, then you have a short circuit on the 5V rail somewhere, but could also be in the 3.3V and isolating the input to IC2 will confirm this. There is not a lot connected to the 5V rail but IC4 or IC3 if the wrong way around could cause it to fail. These things are so small and seeing the align mark for pin 1 needs a good magnifying glass at my age now
Let us know how you get on.