The key is to be able to quickly undo some scary new thing and get back to a known-good point. Also, you need to make sure the testing you are doing is easily distinguished from normal business activities. For us, the humble feature flag is all it took to get unblocked on moving mountains of complex scary things to production. Being able to reassure the customer that we can instantly revert a piece of experimental functionality has been a game changer.
We used to spend months agonizing over how the test environment is such a poor facsimile of production and complaining about vendor XYZ not setting up various things that we would need to prove our code works as expected. We used to make insane bullshit promises about how if things worked well in staging the move to production should be flawless. Those were some dark times for us.