Quiambao won back-to-back UAAP high school championships with the NU Bullpups before playing for the De La Salle Green Archers in the league's collegiate level.

In season 87 (2024), he won his second consecutive MVP award but failed to defend their championship in the finals rematch with the UP Fighting Maroons.

Quiambao's father and grandfather taught him how to play basketball, and he also looked up to the likes of Ryan Buenafe and Marc Pingris.

[7] In a Season 81 win over the UST Tiger Cubs, Quiambao led the team with 13 points, eight rebounds, two assists and two blocks.

[13] In Game 2, he had an all-around performance of eight points, six boards, five assists, and two blocks, and NU won the juniors' championship for the first time since 2016.

[14] Before the start of Season 82, NU successfully defended its ASEAN School Games title, in which they defeated Indonesia for the gold medal.

[16] The Bullpups then swept the FEU Baby Tamaraws in the Finals, with Quiambao contributing in Game 2 with eight points and seven rebounds.

[5] Quiambao had an ugly start to his UAAP career, as he only had five points on 2-of-13 shooting and three steals in a loss to the UP Fighting Maroons.

[29] After spending time with Gilas, he returned to help La Salle break UP's seven-game winning streak with 18 points (13 in the fourth quarter alone) and nine rebounds.

[31] He was unable to play in a crucial game against Adamson as he had tested positive for COVID-19, and La Salle did not make it to the Final Four.

[34] On October 28, 2023, in a win over NU, Quiambao recorded his first triple-double with 17 points, 11 rebounds and 14 assists while also contributing four steals.

In a win over UE, he became the first player in the UAAP men's basketball Final Four era to have logged multiple triple-doubles in one season, as he recorded 17 points, 19 rebounds, and 12 assists while also providing four steals and two blocks.

[41] DLSU began Season 87 with a clutch win over NU thanks to Quiambao's 22 points, eight rebounds, seven assists, and a game-winning triple with 9.8 seconds remaining.

[48] At the end of the elimination rounds, he was the league's leading scorer with 16.6 points, while also being second in free throw percentage (77.8%), and fourth in assists (4.1).

This made him the fifth Archer to win consecutive MVP titles after Jun Limpot (1987–88), Mark Telan (1996–97), Don Allado (1998–99), and Ben Mbala (2016–17).

However, in the second half, he only scored one point as UP denied him the ball and held him to zero field goals made the rest of the way to take Game 1.

[57][58] On December 16, 2024, Quiambao confirmed that he had signed with the Goyang Sono Skygunners in the Korean Basketball League (KBL).

[74] Philippines head coach Tim Cone has lauded his versatility, as he could play more positions for the national team.