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We present the results of ALMA observations in $^{12}$CO($J=2-1$), $^{13}$CO($J=2-1$), and C$^{18}$O($J=2-1$) lines and 1.3 mm continuum emission toward a massive ($\sim 10^6 M_{\odot}$) giant molecular cloud associated with the giant H II region NGC 604 in one of the nearest spiral galaxy M33 at an angular resolution of 0''.44 $\times$ 0''.27 (1.8 pc $\times$ 1.1 pc). The $^{12}$CO and $^{13}$CO images show highly complicated molecular structures composed of a lot of filaments and shells whose lengths are 5 -- 20 pc. We found three 1.3 mm continuum sources as dense clumps at edges of two shells and also at an intersection of several filaments. We examined the velocity structures of $^{12}$CO($J=2-1$) emission in the shells and filaments containing dense clumps, and concluded that expansion of the H II regions cannot explain the formation of such dense cores. Alternatively, we suggest that cloud--cloud collisions induced by an external H I gas flow and the galactic rotation compressed the molecular material into dense filaments/shells as ongoing high-mass star formation sites. We propose that multiple gas converging/colliding events with a velocity of a few tens km s$^{-1}$ are necessary to build up NGC 604, the most significant cluster-forming complex in the Local Group of galaxies.