Is it possible? Yes. Is it likely? Maybe, maybe not.
This is definitely not beyond human ability, but it isn't easy either.
There are about 604 pages in the standard Quran. About 52 weeks in a year. You would have to memorize about 6 pages per week to get it down in two years.
Not only memorize it, but constantly practice it.
Think you can do it? It depends on how hard you try. On top of that, you need to focus on your other daily habits (studying, working) and make sure you dont slack off so that things dont build up.