He was born in 1981 in Üsküdar. After studying at Kartal Anatolian Imam Hatip High School, Topçu completed his undergraduate degree at Sakarya University, Department of Economics and completed his master's degree at Istanbul Medeniyet University, Department of Public Administration. 
He graduated with a thesis on "R&D Project Evaluation Process in Technoparks" and completed his second master's programme at Istanbul Commerce University, Department of Industrial Policy and Technology Management in the same period. 

Topçu worked as Regional Manager in Buffalo, NY - Washington, DC - Minneapolis, MN and Dallas, TX respectively for 3 years in a private company in the USA, then as Import and Wholesale Manager in Hoston, TX, the company headquarters, and then returned to Turkey and worked as Manager and Finance Manager in chain market and automotive sector companies. Between 2016-2018, he served as Advisor to the Minister of Family and Social Policies. In addition to his experience in Ankara, he gained a wide range of international experience with numerous meetings and visits from the United Nations General Assembly to Myanmar Refugee Camps. Topçu, who served as the General Manager of Teknopark Istanbul AŞ between 2018-2023, has been the General Manager of the Turkish Armed Forces Foundation since October 2023.

Topçu, who is a member of the Board of Directors of the World Ethnosport Confederation, Istanbul Commerce University Board of Trustees and DİTAŞ Denizcilik A.Ş. Board of Directors, is married and has 2 children.