  The efficiency of the transport of angular momentum and chemical elements
inside intermediate-mass stars lacks proper calibration, thereby introducing
uncertainties on a star's evolutionary pathway. Improvements require better
estimation of stellar masses, evolutionary stages, and internal mixing
properties. We aim to develop a neural network approach for asteroseismic
modelling and test its capacity to provide stellar masses, ages, and
overshooting parameter for a sample of 37 $\gamma$ Doradus stars. Here, our
goal is to perform the parameter estimation from modelling of individual
periods measured for dipole modes with consecutive radial order. We have
trained neural networks to predict theoretical pulsation periods of high-order
gravity modes as well as the luminosity, effective temperature, and surface
gravity for a given mass, age, overshooting parameter, diffusive envelope
mixing, metallicity, and near-core rotation frequency. We have applied our
neural networks for Computing Pulsation Periods and Photospheric Observables,
C-3PO, to our sample and compute grids of stellar pulsation models for the
estimated parameters. We present the near-core rotation rates (from literature)
as a function of the inferred stellar age and critical rotation rate. We assess
the rotation rates of the sample near the start of the main sequence assuming
rigid rotation. Furthermore, we measure the extent of the core overshoot region
and find no correlation with mass, age, or rotation. The neural network
approach developed in this study allows for the derivation of stellar
properties dominant for stellar evolution -- such as mass, age, and extent of
core-boundary mixing. It also opens a path for future estimation of mixing
profiles throughout the radiative envelope, with the aim to infer those
profiles for large samples of $\gamma$ Doradus stars.
