Quickest? Hmmm... I don't think there is anything you can do to quickly get into Cathay. It is fiercly competetive. Finish your licenses and degree, get the highest quality flight time you can and keep updating your application every few months. Eventually you will get a call. Impress them twice and you are in. Second Officer positions are just as hard to get as First Officer positions at Cathay. It is not because they are less experienced. I have heard of heavy jet captains accepting Cathay SO positions. You say, you can't get 5,000 hours in a few years. There is no magic number on flight time. Some guys get called with a few thousand hours, others have 10 thousand. In my best assumptions, you are still more than a few years away. Things you can do though, other than just building flight time, is become as international as possible. Do your flight instructing over in Asia. Travel internationally, especially Hong Kong, on vacation. Look at getting hired by other Asian carriers until you get called by Cathay. Someone once posted about EVA having a US training program that allowed low time guys going to work for them. Japan has some very good turbo-prop and RJ jobs you may eventually qualify for.
With more than 20,000 applications on file at CX, getting an interview is a lot like winning the lottery, but you can improve your odds. From being one of those 20,000 applications to getting selected, the percentage are in the single digits. So, be careful focussing on only one company. Don't pass up fantastic career opportunities for something that will most likely never happen. (I hope that didn't sound too negative.)
Good luck in your career. One more thing, when I interviewed at Cathay, the one thing all the candidates had in common was that they were extremely positive guys. So as you face setbacks, bumps and bruises along your path to Cathay, keep a good attitude and don't become disgruntled.
Cheers,
BBB