Yeah, depression/burnout is not real. It's just how a person decides to deal with high levels of stress. Stress will not go away. Better deal with it by pushing through it either by working more, going on vacations, sex trips, donations to charity causes, etc.
In the industry I am in - I didn't know anyone, before I started, hell, I even didn't know anyone in the city I moved to. It's all a struggle, endless struggle, like life is supposed to be.
Of course, you need to have conversational skills, soft skills, be able to hold a conversation in different topics, be funny, witty, smart and charming in order to be promoted.
You definetly can get promoted based on your own merrits WITHOUT relying on connections that you had before the job.
The trick is to build your conenctions on the basis of your work, soft skills and charisma WITHIN the company you want to grow.
I am sorry, but with most things in life - climbing the ladder is a competition - success is not guaruanteed, and being good at programming is not the only requirement.