Many quiescent galaxies discovered in the early Universe by JWST raise fundamental questions on when and how these galaxies became and stayed quenched. Making use of the latest version of the semianalytic model GAEA that provides good agreement with the observed quenched fractions up to z similar to 3, we make predictions for the expected fractions of quiescent galaxies up to z similar to 7 and analyze the main quenching mechanism. We find that in a simulated box of 685 Mpc on a side, the first quenched massive (M star similar to 1011 M circle dot), Milky Way-mass, and low-mass (M star similar to 109.5 M circle dot) galaxies appear at z similar to 4.5, z similar to 6.2, and before z = 7, respectively. Most quenched galaxies identified at early redshifts remain quenched for more than 1 Gyr. Independently of galaxy stellar mass, the dominant quenching mechanism at high redshift is accretion disk feedback (quasar winds) from a central massive black hole, which is triggered by mergers in massive and Milky Way-mass galaxies and by disk instabilities in low-mass galaxies. Environmental stripping becomes increasingly more important at lower redshift. C1 [Xie, Lizhi] Tianjin Normal Univ, Binshuixidao 393, Tianjin 300387, Peoples R China. [Xie, Lizhi; De Lucia, Gabriella; Fontanot, Fabio; Hirschmann, Michaela] INAF Astron Observ Trieste, Via GB Tiepolo 11, I-34143 Trieste, Italy. [De Lucia, Gabriella; Fontanot, Fabio] IFPU Inst Fundamental Phys Universe, Via Beirut 2, I-34151 Trieste, Italy. [Hirschmann, Michaela] Ecole Polytech Fed Lausanne, Lab Galaxy Evolut & Spectral Modeling, Inst Phys, Observ Sauverny, Chemin Pegasi 51, CH-1290 Versoix, Switzerland. [Bahe, Yannick M.] EPFL, Lab Astrophys, Observ Sauverny, Chemin Pegasi 51, CH-1290 Versoix, Switzerland. [Balogh, Michael L.] Univ Waterloo, Dept Phys & Astron, Waterloo, ON N2L 3G1, Canada. [Muzzin, Adam] York Univ, Dept Phys & Astron, 4700 Keele St, Toronto, ON MJ3 1P3, Canada. [Vulcani, Benedetta] INAF Osservatorio Astron Padova, Vicolo Osservatorio 5, I-35122 Padua, Italy. [Baxter, Devontae C.] Univ Calif San Diego, Dept Astron & Astrophys, 9500 Gilman Dr, La Jolla, CA 92093 USA. [Forrest, Ben] Univ Calif Davis, Dept Phys & Astron, One Shields Ave, Davis, CA 95616 USA. [Wilson, Gillian] Univ Calif Merced, Dept Phys, 5200 Lake Rd, Merced, CA 95353 USA. [Rudnick, Gregory H.] Univ Kansas, Dept Phys & Astron, Lawrence, KS 66045 USA. [Cooper, M. C.] Univ Calif Irvine, Dept Phys & Astron, 4129 Frederick Reines Hall, Irvine, CA 92697 USA. [Rescigno, Umberto] Univ Atacama, Inst Astron & Ciencias Planetarias Atacama INCT, Copayapu 485, Copiapo, Chile. [Rescigno, Umberto] Univ Andres Bello, Inst Astrofis, Fernandez Concha 700, Santiago, RM, Chile. C3 Tianjin Normal University; Istituto Nazionale Astrofisica (INAF); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Waterloo; York University - Canada; Istituto Nazionale Astrofisica (INAF); University of California System; University of California San Diego; University of California System; University of California Davis; University of California System; University of California Merced; University of Kansas; University of California System; University of California Irvine; Universidad de Atacama; Universidad Andres Bello