One answer is to accept the way things are at BigCo and to just coast along in your role, which is not necessarily a bad thing.
Another answer is to work at an early-stage startup or a small non-tech company where you can move fast. The tradeoff there is lack of job security and lesser pay.
Don't ever expect to move fast at BigCo. It's a BigCo for a reason. By moving fast, you could upset the cash cow, hence the friction placed in front of you. But this can work in your favor. Excellence will not be expected of you at BigCo, and if anyone complains about why nothing is getting done, you just repeat exactly why. As long as the company is making money and you haven't made any enemies, the chances of you getting fired are slim to none.
IMO, you have to look at the big picture. If you ignore the friction factor, is life at BigCo so bad? Are your hours reasonable? Do you like your coworkers? Good pay? Learning to let go your frustration with how you think the company should be run may be the most favorable choice. Remember, all jobs suck, more or less. A year after you change companies, you will find things to hate about that one as well.