External power to start XIAO's program

I just got the XIAO SAMD21 that I coupled via serial communication with the LoRa-E5 module to send sensor data to public network via LoRaWAN protocol.
It’s working if I’m connecting the XIAO directly to my computer via the USB-C cable. But if I’m using an external battery (3.3V) or if the USB-C cable is plugged to a normal plug, only the green light stays ON, but not the blue light for RX/TX transfer with the LoRa-E5 module.
Maybe I didn’t understood well but is this XIAO able to keep programs and to start it with an external power?
Thanks for your help