When I bought my house last year in the LA area I put down about 12 percent. I don’t have a partner or children, and I’m several years older than you are, but in order to make buying a house feasible I had to earn over twice what you make for three years in a row. So no, not impossible for you long-term, but working on growing your career and enjoying your life now is much more important than saving up for a house in the crazy LA market.