Main rulebook, pg. 17, subcategory "Approaching Ice":
"The runner cannot jack out while approaching the first piece of ice during a run."
However, prior to that, on pg. 5, is The Golden Rule:
"If the text of a card directly conflicts with the rules in this book, the card text takes precedence."
Therefore, unless an FAQ contradicts this, I would conclude that the card grants permission to expose the first piece of ice, and if desired, to jack out.
Per your question regarding whether the ice can be rezzed before the runner's Snitch can expose it: in a nutshell, no, the corp may not. Snitch comes into effect during the APPROACH of an unrezzed piece of ice. The timing structure of a run (FAQ page 5) defines APPROACHES as the beginning of Step 2 (effectively, 2.0). The corp does not have the option to rez unrezzed ice until step 2.3.