He was the son of the military, politician and Army minister Charalambos Zymbrakakis (1812-1880).

His elder brother was Emmanouil Zymvrakakis, who also became a Lieutenant General in World War I. Epameinondas enlisted as a volunteer in the army in 1882 and studied at the School of Non-Commissioned Officers, from which he left in 1888 as a second lieutenant.

In 1909 Epameinondas Zymbrakakis was one of the main inspirers and creators of the Goudi coup, as a member of the steering committee of the Military Association.

Also in 1916, when the Provisional Government of National Defence was proclaimed in Thessaloniki by Eleftherios Venizelos, he was one of the first to support it.

After Greece had joined the allies in 1917, he participated at the head of the Serres Division in all the military operations of the Entente, that took place in Macedonia.