Photaki was born in Corinth in 1921 and finished her secondary education at the 2nd Girls Gymnasium of Athens in 1938. In the same year she enrolled at the Department of Chemistry in the University of Athens, where she specialised in Organic chemistry under the mentorship of Leonidas Zervas. Her studies were interrupted during the Axis occupation of Greece when the Laboratory of Organic Chemistry was destroyed and Zervas was imprisoned as a member of the Greek Resistance. Photaki was finally awarded her degree summa cum laude' in 1946 and subsequently continued her postgraduate studies under Zervas, earning her PhD in 1950 with a dissertation regarding glucosamine. Concurrently, she held a paid laboratory assistant position at the university already from 1943, carrying on as a research assistant until 1953.
In 1953, Photaki was awarded a scholarship to conduct research in Basel after examinations by the Greek State Scholarships Foundation. At the University of Basel she worked in the Laboratory of Organic Chemistry, at the time headed by Nobel laureate Tadeusz Reichstein. For the first two years of her stay (1953–1955) she was part of the Max Brenner research group, later moving as an independent scientific associate of Hans Erlenmeyer. Upon returning to Greece, she initially worked at the biochemical lab of the Evangelismos Hospital before being invited by Zervas to the nascent National Hellenic Research Foundation (NHRF) which he had helped found.