how long should it take a new hire to be able to identify good tickets to work on?

How longs a piece of string?

No really, there's so many things that change the answer to that.

What experience do they have?

how big and clusterfucked is the project?

Were they working on something similar before?

Are the tickets well defined, or just 'Make "this" do "that"'
With a lack of detail.

The more positive answers you have to those, the quicker the expected buy in from the new hire you should have.

But in all seriousness, if it's been 2 weeks and still nothing to show for them selves, there's something really wrong.

What if there are no good tickets?

Study the existing system and create a bunch of improvements tickets