According to the relay data sheet it has a 400Ω coil and requires 30mA to operate so, as noted, the relay cannot operate.
If 12V2 is 12V from the power supply output, then I suggest moving C109 to the relay pin 4, and changing the 75kΩ resistor to 75Ω (or one 30Ω resistor).
That would give about a 30ms relay delay as the 12V comes up which should be sufficient to hold the relay open until the surge current to charge the supply filter capacitors has essentially stopped.
And I see no reason for the two relay coil suppression diodes, as the 12V supply will relatively slowly go to zero when the power is turned off, so no significant coil transient will be generated.
Such transients are only generated if the relay coil circuit is suddenly opened when it is energized.
The circuit looks like it was generated by a neophyte engineer at TI.