Clunking noise from exhaust

[Moose]

Hi everyone, hope you're all doing well. Like the title says, when I turn my car on, a clunking/gargle noise comes from the back of my car. It lasts a couple of seconds, then finally goes away as if nothing has happened. I always let my car warm up/ cool down for about 5 minutes before/after driving. This seems to have to do when it has rained, but has happened once or twice on a clear sunny day. Any advice?

 

[Siena]

It's possible one or more rear exhaust mounting rubbers have gone soft, allowing more movement during start-up? I'd check these first, you can get a free check on a ramp, at a lot of exhaist repair / fitting centres.