Brojen was born in the Kuchiamora village of Bikrampur, Bengal Presidency, British India (now Munshiganj, Bangladesh). His father was Harendra Kumar Das. He completed the matriculation exam in 1946 from KL Jubilee High School. He earned his Bachelor of Arts degree from Vidyasagar College in Calcutta.
Since boyhood Brojen practiced swimming in Buriganga River. After his own initiative, the East Pakistan Sports Federation introduced an annual swimming competition in Dhaka in 1953. He was invited to take part in the English Channel Swimming Competition in 1958.
As a part of his training he swam in Shitalakshya River, in lower Meghna. River and a distance of 46 miles starting from Narayanganj to Chandpur. Prior to the competition, he also swam in the Mediterranean Sea from Capri to Naples.
