We combine pulsar population synthesis with simulation-based inference (SBI) to constrain the magnetorotational properties of isolated Galactic radio pulsars. We first develop a framework to model neutron star birth properties and their dynamical and magnetorotational evolution. We specifically sample initial magnetic field strengths, $B$, and spin periods, $P$, from lognormal distributions and capture the late-time magnetic field decay with a power law. Each lognormal is described by a mean, $μ_{\log B}, μ_{\log P}$, and standard deviation, $σ_{\log B}, σ_{\log P}$, while the power law is characterized by the index, $a_{\rm late}$. We subsequently model the stars' radio emission and observational biases to mimic detections with three radio surveys, and we produce a large database of synthetic $P$--$\dot{P}$ diagrams by varying our five magnetorotational input parameters. We then follow an SBI approach that focuses on neural posterior estimation and train deep neural networks to infer the parameters' posterior distributions. After successfully validating these individual neural density estimators on simulated data, we use an ensemble of networks to infer the posterior distributions for the observed pulsar population. We obtain $μ_{\log B} = 13.10^{+0.08}_{-0.10}$, $σ_{\log B} = 0.45^{+0.05}_{-0.05}$ and $μ_{\log P} = -1.00^{+0.26}_{-0.21}$, $σ_{\log P} = 0.38^{+0.33}_{-0.18}$ for the lognormal distributions and $a_{\rm late} = -1.80^{+0.65}_{-0.61}$ for the power law at the $95\%$ credible interval. We contrast our results with previous studies and highlight uncertainties of the inferred $a_{\rm late}$ value. Our approach represents a crucial step toward robust statistical inference for complex population synthesis frameworks and forms the basis for future multiwavelength analyses of Galactic pulsars.