Is it hard wired? If so, and if the alarm module doesn’t have an internal battery, can you go to the breaker box and turn off the circuit it’s on? You should be able to switch off each breaker in turn until it stops if you don’t know which circuit it’s on.

If it doesn’t stop, that means it has a battery backup. But you can still make life more bearable. Switch off all your breakers (you probably have a master breaker for this), then open up the alarm box and either pull the battery or - if it’s non-removable - take the box off the wall, put it in a sealed container, and put the sealed container somewhere… else. Somewhere you can’t hear it or can barely hear it until the battery runs down.

Meanwhile you can turn the power back on but make sure you’ve taped the bare ends of the alarm power cable, or otherwise electrically insulated them, until you’re able to reinstall it.