At 14, he became the youngest Japanese skater to land a quadruple toe loop in international competition with a successful attempt at the event's free skate.

Four days after the junior national championships, he made his Grand Prix debut at 2020 NHK Trophy and placed sixth.

[13] At the Final in Turin, Miura placed third in the short program despite falling on his jump combination, part of a Japanese sweep of the top three placements in that segment.

[19] At the 2023 Four Continents Championships Miura went into the event as one of the favorites for the podium along with Cha Jun-hwan of Korea, Keegan Messing of Canada, and compatriot Shun Sato.

[22][23] Miura entered the World Junior Championships in Calgary as the favourite for the gold medal, and won the short program with a clean skate, placing five points clear of second-place Canadian skater Wesley Chiu.

Referencing his poor short program at the previous year's event, he opined that he was able to "funnel that frustration into a good performance today.

[25] Following what he considered disappointments in the previous season, Miura vowed to change his mindset, with the goal of winning the national title and reaching the World Championship podium.

He worked with choreographer Shae-Lynn Bourne on a free skate to music from Attack on Titan, saying that he would be "acting as if I were fighting as a member of the Survey Corps.

[27] He went on to win his second event, the 2023 Grand Prix of Espoo, coming first in the short program and second in the free skate and beating another Japanese skater, Shun Sato, by 1.22 points.

[28] Struggling with a stomach ailment that curtailed his practice time, Miura finished fifth at the Grand Prix Final for the second consecutive season.

[29] Miura dealt with stomach trouble in the leadup to the short program at the 2023–24 Japan Championships, but managed to place fourth in the segment, cleanly landing all his jumps before two spin errors cost him points.

[31] Miura finished the season at the 2024 World Championships in Montreal, where he came tenth in the short program after failing to execute his jump combination.

Miura was pessimistic afterward, saying: "I feel bad for taking one of the three spots we had at the World Championships due to my poor performance.

[35] Going on to compete at the 2024 NHK Trophy, Miura placed second in the short program where he scored overall 100 points for the first time in an ISU competition.

Despite suffering with pain in his left thigh at the event, Miura made no excuses and was despondent during the interview following the free program.