"first undertook" is correct and usable in written English.
Example sentence: He first undertook the task at the beginning of the month.
Professor Schwartz first undertook a project photographing expectant parents in the nurseries they had created.
AES executives, who first undertook the project in 1994, have found much corruption to confront and vociferous opposition to quell.
He began interviewing scientists and engineers even before entering graduate school, but first undertook large-scale projects while a postdoctoral fellow at the Center for History of Physics of the American Institute of Physics.
When Mr. Suchet first undertook the role in 1987, he prepared a voluminous dossier on Poirot and then synthesized it into 93 character notes, which always accompanied him on set.
Appointed a teacher of astronomy at the École Polytechnique ("Polytechnic School"), Paris, in 1837, Le Verrier first undertook an extensive study of the theory of the planet Mercury's orbit and compiled greatly improved tables of the motion of that planet.
One of his outstanding successes came in the title role of Berlioz's Benvenuto Cellini, which he first undertook at the Holland festival in 1961, then at Covent Garden in 1966, creating some of the decade's – maybe the 20th century's – most compelling sounds in the tenor repertory.
Photography from rockets was first undertaken in 1906.
The calculation, at first undertaken for fun, led eventually to his Nobel Prize work.
The task first undertaken by Henry Withan has now been shared by many observers.
The Perkins interview was one of the first undertaken by the Office.
These were first undertaken by Aston and repeated with increasing precision by succeeding generations.
