Altmaier made his ATP main draw debut as a qualifier at the 2017 Geneva Open, defeating Alexander Ward and Petr Michnev in qualifying. He lost to Sam Querrey in the first round. He won his first ATP tour-level match as a lucky loser at the 2017 Antalya Open when he beat Víctor Estrella Burgos. In the next round, he defeated wildcard Marsel İlhan to reach the quarterfinals, where he lost to Yūichi Sugita. Both of his victories were decided by a third set tiebreak.
Báez has a career high ATP singles ranking of world No. 97 achieved on 22 November 2021 and doubles ranking of world No. 514 achieved on 12 October 2020. Báez has won 8 ITF singles titles and 1 ITF doubles title to date. Báez became the top-ranked junior in the ITF combined ranking on 12 March 2018. Báez made his ATP debut at the 2021 Chile Open where he lost to 2019 Junior French Open champion Holger Vitus Nødskov Rune in straight sets.