I'm a freelancer, so I get to "start" at different companies several times a year, and I'm always surprised by how inefficient things are. However, I'm equally surprised by the fact that a few months in I've forgotten what the bottlenecks were because I've gotten acclimatized.
So by the time I'm in a position to influence those processes I can't remember what the problems were.
What I started doing was take notes the first few days/weeks of what is required to get setup, or where things could be improved. Then I refer back to them every few weeks, and will sometimes up up with solutions and start sending them up the chain.