Adafruit Powerboost latching switch
The EN pin is pulled up through R13 to UBAT. Transistor (see comments above) correctly points out that as soon as the unit is disabled you lose the 5V, if anything the whole circuit is liable to oscillate.
You could try this circuit (I haven't tried it so it would be an interesting experiment).

On power up Q1 is switched ON (due to the small current into its base) taking EN to ground. This keeps the output OFF.
Closing SW1 turns Q1 OFF (Vbe less than 0.6V) allowing EN to be pulled up through R13 (an 'on board component'). The 5V output is now available.
SW1 can be replaced by a second transistor (Q2) which can be controlled by a logic signal. When the input to Q2 is HIGH (Q1 = ON) it turns Q1 OFF, when the input to Q2 is LOW (Q2 = OFF) Q1 is turned ON.
Both transistors are any common small signal NPN types (silicon) e.g. BC548