A hypothetical question.

In term of the construction speed and scale, China is perhaps the No.1 in the world.

It the great wall was considered an infrastructure construction, we may reference to the construction progress of the Chinese High-speed rail in China, which will be 38,000KM in 20 years (2004 - 2025). Since the High-speed rail network would be at least twice or triple difficult than the great wall which does not involve any MEP things (Mechanical, Electrical and Plumbing), we would assume building the great wall would be at least 3 times faster than the High-speed rail road.

Therefore, since the Great Wall of China is 6,800KM, the hypothetical calculated time span would be : (38000 km/20 years) = 1900 km/year, then 1900 km/year * 3 times faster = 5700 km/year , then 6800 km / 5700 km/year = 1.2 year

so, roughly 15 months.

Again, this is very hypothetical.