Can you provide a few more details on what you mean by "management infrastructure"? Are we talking source control / build systems / JIRA workflow stuff here?
I would suggest trying to find ways to be productive yourself that don't involve changing what other people do.
Don't try to sell "ideas" and "proposals", lead by example, and if it works out people will follow.
For example, if people want to use subversion and do their development on trunk, but you want to use git with feature branches... then just do that for your local development, create and switch branches locally all you want, and then push to subversion when you're done.
If there's some dumb JIRA workflow, copy and paste the details to a text file, work on the thing, take your notes in the text file, paste it back to JIRA when you're done. You will probably find you can isolate yourself from most kinds of silliness quite well, and if you're productive doing so then others will follow.
As for your specific question, I think it's worth trying to improve things for at least a year, or maybe two, before you consider leaving. In that time, you'll probably find there are things you can change, learn that other things are actually not as easy to change as you might think, and generally build some useful experience in turning around a challenging situation.