I have only been in this industry for a few years and as far as networking goes, its hit or miss for me. But has generally helped alot. I was not offered jobs simply because of who i know, but they did help me make connections with people at corporations, that led me into the interview.
Now you interview needs to go perfect. thats the key. 2 things. 1. If they dont think your a good fit within their corporate culture you wont get the job. 2. they THINK you are not qualified. you wont get it. Let me explain.
I got hired in a corporate 91 department with 600 total time. flying a few single engines, but right seating in a King Air about 1/5 my 500 hours a year we fly. During the interview, the expressed their desire for a high time pilot for their single engine operations. Due to their HR department usually dealing with hiring shop mechanics, managers, salesman etc. hiring pilots was a new and unknown area. So I made my argument that although you want someone with ATP mins (or what they wanted a 3,000+ hour pilot) to fly a 4 seat single engine airplane will be a hard find since most of them are out in jets, turboprops, etc. But with my CFI/CFII/MEI my training/learning practices are I am much more current and likely on the safer side of habits compared to a guy who has been aerial mapping for 2 years. I also pointed out that total time doesnt mean a good safe pilot, in fact it likely means a higher probability of complacency, and lack of enthusiasm for the job, especially if they are "downgrading" to a smaller aircraft or moving to a small town. (they had a history of pilots only lasting 2-4 months up to this point)
In your case, maybe you dont have the type rating they want or not enough time in a similar airframe. What you could point out is your ability to learn in the aircraft you have flown so far, and that really, besides the size and shape of an airplane. An airplane's an airplane is an airplane. Right? If you can fly a B350, you fly a Cj2 and so on. Put it in words they understand. Can a commercial big rig truck driver drive a large van and a big rig safely? You bet. Its your decision making and learning ability thats more valuable than previous time in type.
At the same time, my "fit" within the company was good. Similar background, similar area of the country, I even had experience working with the products they produce and warehouse/metal shop practices and forklift/squeez clamp truck driving experience. I did not get the job first time around since they hired a guy a little more time and time in both aircraft types and who also was a good fit, but 3 months later I got a call and they had bought another single engine and they offered me the job. I have been here about a year and unfortunately need to move again for family reasons, however I will miss it. I haven't had much of a chance to network except with our other pilots. So my "network" isnt huge, however I have spent sometime learning how to make friends in the right way to lead to these situations. I would recommend you do the same, not just interview prep if you want that sort of thing (i never did, just played the honesty game and its worked well), but talk to someone who you know that really appears to have the networking game down. Thats how i learned most of what I know. Just one friend who was damn good at networking.