Interesting question. I think you would find that the more successful a person is, the bigger their network is. But I believe what you are asking is if that big network is required from the get go. Personally I don't believe you need an extremely big network to be successful, but I do believe you need somewhat of a network established.
To answer your question thoroughly though, you would need to define what you mean by "successful" and what you mean by "big network". I think you would find that the size of your network would also be proportionate to the amount of work you need to put into becoming successful. You never know when you may need help with something, what you may need help with, or who you may need help reaching out to. The larger your network of people the easier it is to do those three things.
