Cruz joined Primera División Paraguaya club Olimpia Asunción's youth academy at the age of nine, where he became the top scorer during several seasons. The club's first-team coach, Luis Cubilla, invited Santa Cruz to train with the team aged 15, and the player eventually made his first-team appearance in the 1997 Primera División Paraguaya at the age of 15, during the Torneo Clausura on 27 July when he entered the field in the 80th minute for Alfredo Mendoza in the Paraguayan derby against Cerro Porteño. 1998 season During the group stages of the 1998 Copa Mercosur, Santa Cruz scored his first goal of the competition in the 11th minute of Olimpia Asunción's 4–2 away victory against Argentine side Racing Club on 14 October 1998. The club finished in second position of their group with ten points, and advanced to the quarter-finals to face José Luís Chilavert's Vélez Sársfield. During the first-leg of the quarter-final match on 27 October, Santa Cruz scored in the 65th minute of Olimpia's 4–3 away victory. One week later, Santa Cruz scored a brace for Olimpia as they claimed a 2–1 home victory in the second leg on 4 November 1998. His goals came in the 24th and 40th minutes of the first half. All of his three goals were scored against his international teammate Chilavert. Bayern Munich's eyes looked at Santa Cruz for the first time after he scored his double past José Luís Chilavert. The club was later eliminated from the competition at the semi-final stage by Palmeiras, who would go on to win the tournament. During the 1998 Primera División Paraguaya season, Santa Cruz scored three goals in nine appearances as Olimpia were crowned champions of the league. The club had also reached the knock-out stages of the 1998 Copa Libertadores, where they were eliminated by Argentina's Colón. 1999 season During the 1999 Primera División Paraguaya season, Santa Cruz scored 10 goals in 14 appearances as Olimpia claimed the league title. Santa Cruz participated at the 1999 Copa Libertadores, where Olimpia were drawn in Group 3 with Cerro Porteño, eventual champions Palmeiras and Corinthians. In Olimpia first group stage match, against Cerro Porteño on 24 February, Santa Cruz scored a second-half double past Aldo Bobadilla in the 58th and 89th minutes as his side were defeated 4–3. On 5 March, Santa Cruz played a full 90 minutes in his side's second group stage