How quickly can you build your credit score?

[Isaac Hemingway]

I'm 18 years old, just got my Bachelor's Degree in Business (I graduated from High School at 15), have no credit score, 20K saved up, a full-time job, and am looking to buy a home for 200K or less (I live in an area conducive to this). 

How quickly can someone as young as me build a credit score into the 700s starting from a non-existent credit score?

Or, would I be better off getting a manually underwritten mortgage that requires no credit score (from a company like Churchhill mortgage)? 

Thanks!