The road is to be used to resupply a city siege.
The best estimate of speed for how fast the Roman's could build a road I can find is their construction of the Appian Way or "Queen of Roads". This road is 20 feet wide and 132 miles long, and was completed in approximately 11 years, translating to a construction speed of one mile a month.
I don't have information on the size of the work crew or if they worked at night at all, but I'm going to assume work time on the road being equivalent to our 8 hour work day, the rest of the time being spent training, eating, etc...
I assumed a proportional number of workers would be building roads on my world. The population of the Roman Empire was estimated at 56.8 million, and the population on my world focussing on building the road is 500 million. Which equates to 8.8 times faster for each construction lead. If it was only one road construction lead, 2 years 10 months to finish.
War time speed I assume to be 24/7 construction by three construction teams. That reduces the time to 1/3 at 11 months and 13 days. My world has resource locations enough for 3 construction leads, which brings the final completion speed down to just 3 months and 24 1/2 days. Does that speed sound reasonable?