How to use a proximity sensor with a solenoid
It's clear that the sensor is incapable of sourcing 1.1A required for the solenoid to actuate.

However, it's capable of lighting the LED and the voltage that's being read is the forward voltage of the LED.

A transistor driving a relay and a 5V DC power supply capable of sourcing 1.1A would be additionally required to actuate the solenoid.

Here's the schematic.