Oliver Basabe was born in Venezuela and grew up in a family of ballplayers. His cousins Osleivis and Luis Basabe have played major league baseball for the Rays and Giants. His brother, Osman Basabe, played in the 2023 Little League World Series and named Olivier as his role model. Oliver came to the States to play college baseball at Indian Hills Community College and would transfer to Faulkner University.  

Basabe had a .342 average with 20 doubles in his lone year at Faulkner and drove in 39 in 65 games. This performance caught the eye of the San Diego Padres, who used their 8th-round pick in the 2017 draft to select Basabe. The 27-year-old was a utility player in the San Diego system, serving time in the outfield and all infield positions.   

Basabe played his first season in the American Association in 2023 with the Kansas City Monarchs; midway through the year, he was traded to the Kane County Cougars, where he finished playing the last 50 games of the year. That season, he had a .293 average, added seven home runs, and collected 16 doubles. He was traded to the RailCats last offseason to complete a trade for Michael Woodworth.  

Basabe quickly became an everyday third baseman for the RailCats in 2024. He was featured in 99 games and led the team in doubles, RBIs, and triples. Basabe also added some value with his defense, finishing second in assists recorded for a third baseman and leading with 86 putouts.