LMR10510 - Simple switcher "breakoutboard" output measures 0V
You've used the wrong pin-out for the device. The pin-out you've used is (somehow) partly for the WSON package but you've got a SOT-23 on the PCB: -



On your PCB you have pin 1 connected as if it were the FB pin yet, for a SOT-23 pin 1 is SW etc...

You also don't appear to have GND (pin 2) connected (I've highlighted it in green): -