Wlk played at Club Nacional as a child but started playing for Club Olimpia from the age of 14 years old. He broke numerous goal scoring records as a teenager including one period where he scored 130 goals in 3 seasons of youth football. He signed a professional contract with Olimpia in 2021 lasting until 2025. He made his league debut for Olimpia on 12 March 2023 in a 2-1 win against Club General Caballero JLM.
Wlk was the tournament top scorer as Paraguay won gold at the 2022 South American Games held in Paraguay between 4 and 12 October, 2022. His haul at the games of six goals in five games included a hat-trick against Peru. He also scored the only goal in the final as Paraguay beat Ecuador 1-0. Wlk was quoted as saying after the final; “This achievement is something unique that I will never forget, at the time I could not measure what we had achieved. I am very proud of this great group because we gave everything and we were fair winners of this gold medal”.
His father is called Cristhian Wlk. Regarding his surname Wlk was quoted as saying to the radio stationUniverso 970AM "My great-grandfather came from the Czech Republic after the war, he arrived and settled in Colonia Independencia, I often visit the place."