You can get there in six months or never. The joys of horses!
Speaking in gross generalizations (JMHO)
Four big facets of any horse: physical soundness, athleticism, mind, quality of training
Four big facets of any rider: physical soundness, athleticism, mind/grit, access to training
At one end of the spectrum you have a horse that is sound with a lot of maintenance, 5/10 gaits, a tricky and reactive mind, who can get through a 4th level test when ridden very precisely. This horse is paired with a rider who has normal aches and pains, desk jockey level of fitness, is easily overwhelmed, and can only lesson once a month. The odds of this rider scoring a 60+ at 4th level is slim and will be an uphill battle mostly because of the horses mind and lack of access to training.
At the other end of the spectrum is a spotlessly sound horse with 8/10 gaits, a workmanlike and bombproof mind who finds the grand prix work easy. This horse is paired with a physically sound rider with a high level of both fitness and flexibility, brave with lots of grit, and is in 5 day a week training. This pair could go from 1st to 4th level in a season with scores well into the 60s. I know riders who have access to international quality schoolmasters and receive multiple lessons a day. They went from 1st/2nd to FEI in 2-3 years and are scoring in the high 60s to low 70s at Wellington.
If I had to pick the one non-negotiable it is the mind. Find a schoolmaster who doesn’t mind mistakes and has a forgiving nature. With access to regular training progress can be much quicker than a more athletic horse who has a short fuse or gets flustered with incorrect aids. An 8 mover with a phenomenal mind and a FEI record is typically the price of a nice house but a 6 mover can be much more affordable.