Multisim - Circuit Design with a 555-timer
Forget the 555, use a counter instead. Here's a project that does exactly that, as a complete design: https://www.electronics-lab.com/project/long-duration-timer/

Or use a microcontroller. ATTiny would be ideal for this - it has an internal oscillator so all you need is the switch to trigger it and the driver transistor for the relay (hint: use an N-FET and drive on the low side. It's easier.)

Or if you follow Marcus' link, a non-555 approach to 555 problems written by some guy.