[4] In July 2015 Galvão and his sister left the country for the first time, to participate in the American National Jiu-Jitsu Championship taking place in Las Vegas.

[14] At 15 Galvão was promoted to blue belt, winning the 2017 IBJJF Kids Pan; a month later, during a tournament known as Copa Podio Orange League Event where juveniles faced experience grapplers, Galvão submitted Leandro Rounaud, a former IBJJF Manaus Open adult black belt champion.

[15] In January Galvão won the IBJJF European Jiu-Jitsu Championship taking place in Portugal, in the Juvenile, blue heavy division.

[19] In May 2021 Galvão participated in Flograppling's Who's Number 1 (WNO), defeating World No-Gi black belt Champion and ADCC veteran Dante Leon by unanimous decision.

[20] In June 2021 it was announced that Roberto "Cyborg" Abreu's Fight Sports was partnering with Melqui Galvao's project in Brazil providing an exchange program between their HQ in Miami and their location in Manaus.

[3] That same year, as a Brown Belt, Galvão won the Abu Dhabi Grand Slam World Pro and the 2021 IBJJF No Gi Pan Championship in the middleweight division.

[11] On 19 June 2021 Galvão entered the Third Coast Grappling 7 grand prix, submitting three BJJ black belts in one night to win the title.

[24][19] After defeating Carlos Andrade at the prestigious Curitiba Open, a tournament featuring the top Brazilian competitors, Galvão held a record of 12 submission win in a row.

[27] In April 2022, Galvão took part in BJJ Stars 8 Middleweight GP, one of the biggest and most prestigious professional jiu-jitsu shows taking place in São Paulo; Galvão won the first match against multiple-time black belt World champion Leandro Lo via decision, the semi-final against Mauricio Oliveira via submission (Injury Forfeit) then won the final against Lucas "Hulk" Barbosa, a-two time World champion (Gi and No-Gi) whom Galvão defeated with a Bow and Arrow Choke.

[30] In January 2023, Galvão's father Melqui announced that they would be separating from Fight Sports and branching out as their own BJJ affiliation, including a new location in São Paulo.

[31] He returned to gi competition for the first time in 9 months at the Abu Dhabi Grand Slam Tour in London on 12 March 2023, winning gold in the welterweight division.

[32] Galvão was then booked to compete in a superfight against Alexandre de Jesus in the main event of Majestic BJJ 3 on 1 April 2023.

[35] He defeated Otavio Nalati on points in the opening round before winning his quarter-final match against Kaynan Duarte by disqualification.

[40] Galvão made his return to competition after recovering from his injury at the CBJJE Sao Paulo open 2023 on 29 July, winning a gold medal in the medium-heavyweight division.

[46] Galvão was scheduled to make his first Who's Number One welterweight title defense against Kody Steele at WNO 21: Ryan vs Barbosa on 30 November 2023.