Modern disc galaxies commonly have distinct thin and thick discs that areseparable in some combination of their kinematics, radial structure, chemistryand/or age. The formation mechanisms of the two discs and the timing of theironset remain open questions. To address these questions, we select edge-ongalaxies from flagship JWST programs and investigate their disc structures inrest-frame, near-infrared bands. For the first time, we identify thick and thindiscs at cosmological distances, dating back over 10 Gyr, and investigate theirdecomposed structural properties. We classify galaxies into those requires twodiscs (thin and thick discs) and those well fitted by a single disc. Discradial sizes and vertical heights correlate strongly with total galaxy massand/or disc mass, independent of cosmic time. The structure of thick discsresemble discs found in single-disc galaxies, suggesting that galaxies form athick disc first followed by thin disc formation. The transition from single todouble discs occurred around 8 Gyr ago in high-mass galaxies ($10^{9.75} -10^{11}M_\odot$), earlier than the transition which occurred 4 Gyr ago inlow-mass galaxies ($10^{9.0} - 10^{9.75}M_\odot$), indicating sequentialformation proceeds in a "downsizing" manner. Toomre $Q$-regulated discformation explains the delayed thin disc formation in low-mass galaxies,leading to the observed anti-correlation between the thick-to-thin disc massratio and total galaxy mass. Despite the dominant sequential formation,observations suggest that thick discs may continue to build up mass alongsidetheir thin-disc counterparts.