Chances are though, these terms are already part of their original employment agreement in some way (as allowed by the relevant laws in the state). That said, non-competes are court-tested and the business may not be interested in expelling more resources to prevent competition when they could just make a new contract not tied to their employment.
The so-called "Gardening Period."
This is very untrue. You could agree to sign a non-compete or NDA after the fact, agree to be on retainer for consulting, or agree not to quit on the spot.
Learn their standards, policies, and exceptions-- ask for exceptions!
On this subject, Stuart Diamond is the master. Here is his presentation @Google > https://www.youtube.com/watch?v=ZOZo6Lx70ok
Read the book!