Educated at Durham (N.H.) Academy and Norwich (Vt.) University, Dodge graduated as a military and civil engineer in 1851, just when railroad building was beginning in the United States on a large scale. During the American Civil War he was promoted rapidly to the rank of brigadier general of volunteers and provided valuable service in bridge and railroad construction. For example, he built a bridge 14 feet (4 m) high and 710 feet (216 m) long across the Chattahoochee River in only three days.

From 1866 to 1870 Dodge was chief engineer for construction of the Union Pacific Railroad. In 1873 he joined Jay Gould in railroad development in the Southwest and in the next 10 years helped build nearly 9,000 miles (14,500 km) of track in the United States.