AFTER the first cable end is connected is when the timer starts.
After you enter the room with the massive drill in the center get all the cables into the connector room. Green is on top off the far tan room. Blue is in that room under green. Yellow is in the middle of the floor. Red is in the connector room up the stairs. After the first cable end is connected the 35 seconds counts down. Connect all 8 ends of the cables into the correct colors and as long as you do it under 35 seconds it will pop. This may be easier in coop but is definately doable solo.
*edit* thanks to elquietone if not done under 35 seconds you can pull all the wires out and then try again without having to reload checkpoint or level