I think that timing chains can stretch on these engines, maybe it's the tensioner taking up the slack when it goes quiet.

Sounds like the hydraulic tappets coming up. With that sort of milage they'd be a fair way past their best and I'd expect them to rattle like billy-ho on a cold start.

When were the oil and filter last changed? Fresh oil would help to alleviate the starting rattle. Also here, on those ecotec engines even a slightly low oil level makes a massive difference. Make sure it's up to the maximum mark on the dipstick.