In 2014, after giving up only one walk for the duration of the season, he began to attract the attention of the Phillies organization, and he was moved to the Rookie League the following year.

In 2017 and 2018, he continued to rise through the Phillies' farm system, spending time in Double-A and Triple-A as a starting pitcher with a high strikeout rate.

He returned to the team in 2021 as a long reliever, pitching a stretch of successful middle innings in a depth-challenged roster, before joining the starting rotation at the trading deadline.

[3] He was sixteen years old when he made his professional baseball debut for the Venezuelan Summer League (VSL) Phillies, pitching in three games as the team's closer.

[4] Suárez' season came to an abrupt end in July after he was found in violation of the Minor League Baseball (MiLB) drug program.

[14] In 2018, Suárez was assigned to the Double-A Reading Fightin Phils as part of a starting rotation that also included Romero, Kilome, and Seranthony Dominguez.

[4] After a rain delay forced a doubleheader against the San Diego Padres, the Phillies needed an extra man in their starting rotation, and Suárez was called up to the major leagues on July 24, 2018.

[1] Despite playing 82 of his 94 minor league games as a starting pitcher, Suárez became a staple of the Phillies' bullpen as a left-handed reliever alongside Morgan and José Álvarez.

[24] After spending four weeks quarantining in a hotel room in Clearwater, Florida, Suárez rejoined the roster for the final part of the season, which was shortened to 60 games due to the impacts of the pandemic.

[25] He began rehab assignments in Lehigh Valley in late August before being placed into a bullpen with recent acquisitions Brandon Workman, Heath Hembree, and David Hale.

After the 5–2 victory over the Washington Nationals, Phillies manager Joe Girardi told reporters that he intended to combine Howard and Suárez in future games.

[28] His role had shifted by July: Héctor Neris was removed as the Phillies' closer in June after four blown saves and an 8.22 ERA for the month, and José Alvarado lost the position when he walked 27 batters in 31 innings.

[30] At the MLB trading deadline, the Phillies acquired closer Ian Kennedy from the Texas Rangers; Suárez, in turn, was promoted to the starting rotation.

[31] Suárez threw his first career complete game, a 97 pitch four-hit 3-0 shutout or Maddux against the Pittsburgh Pirates on September 25, 2021.

Suárez entered the game in the top of the ninth inning to replace David Robertson, who managed to strike out his first batter and issued two walks afterwards.

With two outs, Suárez faced Austin Nola, who hit a fly ball on the first pitch thrown and was caught by Nick Castellanos, claiming a 4–3 victory over the Padres.

During that period, Suárez won all six of his starts with a 0.63 WHIP, a 1.32 ERA in 41 innings pitched, and a complete game shutout against the Colorado Rockies.

[38] Suárez spent most of his professional baseball career as a starting pitcher before alternating through the bullpen in many roles such as a long reliever, set-up man, and closer by the Phillies from 2019 to 2021.

[39] Suárez' pitch repertoire varies based on how he is being used: as a starting pitcher, he prefers to use a slider, while, as a reliever, he utilizes a combination of a sinker and a changeup.