I'm looking for an idiom - if one exists - similar to "sink or swim", but describes when someone must learn quickly (say a new job) because they are being faced with the actual experience
I'd say thrown in at the deep end is about as "similar" to sink or swim as it's possible to get.
Google Books says there are over 30,000 hits in that link - and without actually looking, I'm prepared to bet most of them are for OP's figurative sense, not the literal one.
Here are a few:
- she has to succeed or fail on her own merits
- the training wheels are off
- he's in the major leagues now
- there's no safety net
- he's on his own now