Only way to code under pressure like that is with practice. I turn into an idiot non-coder in these situations, but I've gotten much better over time, to where I always pass a live coding session. In the real world, I spend a fair amount of time thinking and teasing a problem apart before I actually start coding. This is hard to do in an interview - even if the interviewer says "think about it for a few minutes", they will inevitably step in and offer a suggestion after 30s of silence. It's like you have to code by pure instinct. Which is doable with practice. But it's hugely skewed towards people who have the time or desire to practice such things.

This is why advice for passing the Google/etc. interview usually boils down to: Quit your job for a month and do competitive coding, and you will pass with ease.