Understanding the Milky Way disc formation requires characterising its structural and kinematic properties as functions of stellar age. Using red giant stars from APOGEE DR17 and Gaia DR3, we model the age-dependent stellar kinematics with a quasi-isothermal distribution function and fit disc parameters as a function of age using non-parametric splines. We identify a transition from thick to thin disc populations around 10 Gyr ago. Stars older than this have short scale lengths (∼1.7 kpc)...