I don't get how people get jobs so easily. It took me like 8 months and it was extremely stressful.
Smaller teams are also more tight-knit so recommending a new potential dev wasn't a matter of process - it was literally head down a few doors and have a chat with the director.
I'm sure it's significantly different for huge enterprises where even the teams within the R&D department are heavily siloed.
If your manager is inexperienced or not very good then there's nothing you can do about that.
I haven't worked for any massive companies with thousands of employees where there might be a lot of bureaucracy, but the few I've worked for ranged from ~100-700 and it was pretty easy to get interviews for referrals. One of my employers encouraged referrals and offered bonuses if it led to a hire.