Being an UI designer is not an easy task. It takes years of experience and patience until you are recognized in the business world. Even after then, you will have to compete with other experienced designers and triumph. One cannot simply be a great designer in matter of seconds. One cannot also be a great designer by graduating from top universities. It is all about the years of practice and learning.
First step to getting into the UI designer's world is to apply for the job that matches your qualification. Just because you have graduated from the top university in the world does not mean you will be the best designer. There are countless numbers of other designers that have graduated from same university or have even greater skills. Therefore, you will have to start from the bottom and learn from the experienced designers. Learn their skills and make it your own.
Also, do not give up just because you are not hired. Keep on being persistent. This is not applied just to the UI designers. many jobs in this competitive world require persistence. Many will be rejected the first time they apply for the job. Some will be rejected continuously. However, in the end, you will manage to find the job that will fit you.
Be willing to work as a freelancer. Freelancer is a job that can open up for your future career. Even if the initial pay as a freelancer might be minimal, it will eventually stack up to something greater. Not only those it provide experience to the business head-on, but also create new connections. Connections are important as a designer. Someday, the certain business can remember you and use you for the future use after working together. This chain of connections can stack until you can be the most demanded designer in the market.
Being a designer is not an easy task. However, it never means that one should give up on the dream. It is all about the persistence and experience that will eventually be caught up. Never give up on the dream that was never attempted. Keep on learning and stay competitive.