I do 1-70 in overnight+ couple of hours next day.
I don't know if its the fastest, but works for me. Remember to spend all your paragon points, and use the armory plugin to automatically equip better gear. I use the act1-5 profile on normal difficulty. It's close to 100% solo-able if you have like 150-200+ paragon points. After that, I use the (now outdated cuz of leg nurf) legendary road profile on hard difficulty until it reaches level 70. At the time you hit level 70 you should have good rares and a couple of lower level legendaries and should be able to do Ghom on t1. If not, run Ghom a couple of hours on lower difficulty, and move as fast as you can up to t1.
Because a lot of highend legs only drops on t1-6. On my wizard I was not able to do t6 right after I hit 70, but on my WD I was able to do t2-t3 at the time I hit 70. So it depends on what class you are. Some are just better than others against Ghom.