Here is very simple circuit in which the LED becomes ON only after a preset time the power supply is switched ON. When the power supply is switched on the transistor will be OFF. The capacitor now charges via the preset R3 and when the voltage across C1 is sufficient, the transistor switches ON and LED glows. The ON delay depends on the value of P
OT R3. You can increase the time delay by increasing the resistance of POT R3.