Will acquiring Korean nationality and the birth of an illegitimate child be a problem?

Question

Hello! I was born in Mexico, and my father is Korean while my mother is Mexican. I am currently 24 years old, and at the time of my birth, my parents were not married. They only registered their marriage in Mexico and also reported my birth there. I was born in October 2001, and my parents registered their marriage in March 2002. In this situation, will there be difficulties in obtaining Korean nationality? I am curious if being born out of wedlock will have any impact.

I would like to know what procedures and documents are necessary for the process of acquiring Korean nationality, and I would also appreciate advice from those who have had similar experiences. I am particularly interested in hearing from people who have gone through this process in areas like Seoul and Gangnam. Thank you!