[6] The year after, Minì mainly competed in international competitions, he became champion in the WSK Super Master Series, beating then Mercedes Academy driver Paul Aron among others, and finishing as runner-up in the CIK-FIA Karting World Championship.

[11] Minì started his season off strongly by scoring all three pole positions at the first round in Misano,[12] winning his first ever race in single-seaters.

[17][18] In the second Imola round, a triple podium which included another win enlarged the points gap to his nearest rival Francesco Pizzi,[19] such that a second-place finish in race two allowed Minì to be crowned champion of the series.

In December 2020 Minì took part in the post-season rookie test for the Formula Regional European Championship for ART Grand Prix alongside his F4 title rival Francesco Pizzi and Grégoire Saucy.

[28][29] He started his season off by scoring his first points in race 2 of the first round, with a sixth place also giving him the distinction of being the highest-placed rookie.

In the pre-season, Minì joined Hitech Grand Prix to partake in the Formula Regional Asian Championship.

[38] He ended his campaign strongly with another win and a podium finish in Yas Marina, lifting him to fourth in the standings with 130 points.

[42][43] He was stripped of his first win during the first race due to a false start,[44] but secured redemption the next day in the wet with a first victory.

[45][46] Following a Monaco rostrum,[47] Minì triumphed in Le Castellet, holding off championship leader Dino Beganovic for his second win.

In September 2022, Minì took part in the FIA Formula 3 post-season test at Jerez, driving for Hitech Grand Prix, setting the fastest lap during the first day.

[57][58] Minì ended up driving for the team during the 2023 FIA Formula 3 season, partnering Luke Browning and then Red Bull junior Sebastián Montoya.

[64] In a relatively straightforward feature race, Minì defended third place against Leonardo Fornaroli during the closing laps to clinch his first Formula 3 podium.

[68][69] A scoreless round at Barcelona followed; he collected a penalty for spinning Christian Mansell out in the sprint, while he lacked pace in the feature race.

[71] However, his fortunes took a reverse turn on Sunday as he retired on the opening lap due to contact with teammate Browning.

[77] However, Minì failed to score at Spa despite qualifiying third;[78] he was involved a collision with Pepe Martí on Saturday for which the Italian received a five-place grid penalty,[79][80] and not being able to start on Sunday after crashing on the sighting lap.

[99][100] He proceeded to fend off Christian Mansell, helping him to get back-to-back feature race wins in Monaco; in doing so he took the championship lead.

[101][102][103] At the next round in Barcelona however Minì went pointless, as he retired from the sprint after contact with Sebastián Montoya and dropped positions during the feature.

[104][105] Qualifying fourth in Austria,[106] Amidst many fights, he fought his way back to sixth place in the sprint race.

[108] Another tough qualifying followed in Silverstone with 14th,[109] After a super start in the sprint race, Minì battled with his fellow Alpine junior Nikola Tsolov, but came up short and finished sixth.