If you are transitioning from push to pull, start off by identifying a work area with relatively few problems and low risk to start learning about pull. Do a trial run to develop confidence in whatever methods you establish.
Use the trial run to identify problems, and then work on eliminating those issues before going live.
Consider creating a safety stockpile of products to draw from when the inevitable problems occur, but then make sure you consume them when the new system is established.
Focus on building systems before rolling pull out company-wide. You’ll find that early pull systems need quite a bit of refinement. You’ll save time if you roll out a finished process rather than a beta version. You are better off creating a strong infrastructure before you remove the safety nets.