* Network with the smart people that the BigCo's HR has carefully vetted for you. Specifically, find the ones that share your interests and may want to found a startup together.
* Hone your presentation skills in numerous meetings.
* Make contacts to other companies and learn about some business models previously unknown to you.
* Put aside enough savings to not need a paycheck in the foreseeable future.
You need to be careful abiding the non-compete terms, but generally try to end up with a very solid understanding of some business problem you would want to solve with your startup, and a network of people with mutual trust that would gladly join you on your new cause.
Also be careful to not burn the bridges with BigCo, since most startups fail, bla bla, yada yada.
I would advise against joining a random startup as a rank-and-file employee. You won't have the same level of trust with the founders, as you could have with your ex-colleagues, and you will likely just spend working crazy hours making someone else's dream come true, only to get screwed with equity dilution once the startup hits the exit.