No Stupid Questions

I'm assuming your question pertains to a window failure while still on the airport grounds prior to takeoff. If instead you meant a window failure while at cruise, I would suggest this Mentour Pilot video about Southwest Flight 1380 where an engine defect threw shrapnel at one of the cabin windows, smashing it open with disastrous effects.

Supposing the window failed prior to opening the jet bridge to allow passengers to board, it probably would have been noticed by the flight crew -- ie the pilots, cabin staff -- while doing their preflight preparations and checks, or by the ground crew, while loading baggage or food/supplies. Once notified, the boarding process would be delayed as the pilots assess whether the flight can continue -- definitely not -- and then the captain would use their authority to reject the aircraft for that flight, calling in the maintenance team and the airline so they can take the next steps. Practically speaking, this flight will be either heavily delayed or outright cancelled.

If instead the window failed after closing the doors and the aircraft has started taxiing to the runway, then there are some complications. With everyone seated for taxiing, passengers are not supposed to start walking around to notify the cabin crew. But the cabin crew may already be walking the aisles to check for stowed trays, seatbelts for takeoff, baggage obstructions, etc. So if they see a smashed window, that's an obvious sign that the cabin is not secured for takeoff. At the end of the cabin checks, the cabin crew would normally telephone the pilots to convey a secure cabin. Here, they would explain the situation and the pilots would contact ground control to return back to the terminal.

But supposing the window broke after the cabin was declared secure, and the aircraft is about to line up onto the runway. In this case, everyone including the cabin crew are sat down, so a passenger who sees the window can't really get the cabin crew's attention by pressing the overhead button. Barring some sort of additional malfunction that the pilots could notice -- like a major engine malfunction -- this aircraft might actually take off.

When taxiing, the pilots have a number of things to do, and so the "sterile cockpit" rule means that no non-operational chitchat is allowed, to allow them to focus. Mentour Pilot has other videos on what happens when the rule is violated. Likewise, the cabin crew are trained to not disturb the pilots unless something absolutely flight endangering is happening, at least for the first few thousand feet of takeoff climb.

The theory is as follows: if an aircraft is on the ground and stationary, it is safe. If the aircraft is at cruising altitude and cruising speed, it is safe. But if it's at low altitude (<1000 ft; 330 m), then it's very easy for the flight to go sour. Hence, once an aircraft has reached a certain point in taxiing, it will basically want to take off. And we still have the problem that the pilots don't even know the window broke.

So the aircraft rolls down the runway and takes off. Crisis? Not really. The plane will climb quickly up to some 3000-5000 ft, at which point the plane is configured for a steady climb to cruise. This is when the pressurization system would engage, since cabins need to keep the pressure to a breathable level. Although the system may also have noticed that the cabin pressure stayed the same as the outside air pressure for the entire climb. That's a clear sign of a cabin air leak, and the system would indicate to the pilots of a pressurization failure.

This is the first indicator for the pilots, although at this stage in the flight, the cabin crew may also phone the pilots since they start walking around earlier than 10,000 ft altitude. A pressurization failure or broken window means the pilots must halt their climb and remain below 10,000 ft, which is the upper limit for human breathing without supplemental oxygen. The pilots would radio to ATC and request a return to the airport, or another nearby airport if need be. A pan-pan or mayday could be declared, depending on the captain's assessment of the situation, or to obtain priority over any other aircraft wanting to land.

The last scenario before the Flight 1380 scenario is if the window broke just as the aircraft was passing 10,000 ft altitude, so there was no earlier indication of a cabin leak. In this case, there will indeed be a cabin depressurization, although it won't be as severe as at cruise altitude. Some aircraft will automatically drop the oxygen masks, and the pilots will don their own masks, now cognizant that a full-blown emergency is underway. This is handled the same way: bring the aircraft down to a breathable altitude and call ATC. The oxygen masks are good for some 20 minutes, which is well more than enough time to return to a lower altitude and make a plan.

TL;DR: the entirety of Mentour Pilot's YouTube back catalog truly sheds light on how the aviation industry keeps people safe. I highly recommend.