Several years ago I invented something that I called 2-Law of Desperate Workers:
Law 1: To get a better job, you need to have good experience and build good working experience profile
Law 2: In order to get good experience and build good working experience profile, you need to work in a better job
So you are not happy with your current workplace because it doesn't offer good experience. You want to move to a better company, but they are looking for someone with good experience. And to get that good experience, you need to work in a better company.
You can use professional certification like CCIE to remedy the 2 Law issue. Taking CCIE lab won’t give you large scale deployment experience, but at least it’s close enough to teach you about some design aspect, setup and troubleshoot complex technology in much smaller scale. And it can show your willingness to learn, your self-discipline during the study, and your ability to tackle such difficult challenge. Obviously once you are able to move to a better job with your CCIE, you need to start getting the real good experience.
The other way is by making connection and helping others in the community like Project Avatar. Not only it can give you more experience in leadership, coaching skill, and teaming up with others, it will also make people recognize you and it would be easier for them to give you reference (remember, it's 'who knows you' that matter).
It's not easy to write to share your knowledge. It takes effort to answer other questions or to conduct live presentation over web conference. But if you are willing to do so, you will build a stronger profile and get additional experience that you may not be able to get at your current workplace. And all the experience and reference you make now may help you in the future.
So help others to help yourself. Let's start it on Project Avatar.