The paper presents a simulation-based inference (SBI) analysis of cosmic shear data from the KiDS-1000 survey, focusing on the two-point statistics of weak gravitational lensing. The SBI method efficiently performs non-Limber projection of the matter power spectrum and constructs log-normal random matter fields on the curved sky for various cosmologies, including intrinsic alignments and baryonic feedback. The forward model samples realistic galaxy positions and shapes, incorporating shear measurement uncertainties, redshift calibration, and angular anisotropies due to variable survey depth and point-spread function variations. The analysis uses pseudo-angular power spectra as summary statistics and employs neural density estimation with active learning to infer the posterior distribution of spatially-flat $\Lambda$CDM cosmological parameters from 18,000 realizations. The results yield a marginalized mean of the growth of structure parameter $S_S = 0.731 \pm 0.033$ (68\%). The forward model fits the data well with a probability-to-exceed of 0.42, and the constraints are wider compared to a Gaussian likelihood analysis due to cosmology dependence in the covariance. Neglecting variable depth and anisotropies in the point spread function can lead to an overestimation of $S_S$ by about 5\%. The findings are consistent with previous analyses of KiDS-1000 and highlight a 2.9$\sigma$ tension with early-Universe constraints from cosmic microwave background measurements. The work underscores the importance of forward-modelling systematic effects in upcoming galaxy surveys like *Euclid*, *Rubin*, and *Roman*.The paper presents a simulation-based inference (SBI) analysis of cosmic shear data from the KiDS-1000 survey, focusing on the two-point statistics of weak gravitational lensing. The SBI method efficiently performs non-Limber projection of the matter power spectrum and constructs log-normal random matter fields on the curved sky for various cosmologies, including intrinsic alignments and baryonic feedback. The forward model samples realistic galaxy positions and shapes, incorporating shear measurement uncertainties, redshift calibration, and angular anisotropies due to variable survey depth and point-spread function variations. The analysis uses pseudo-angular power spectra as summary statistics and employs neural density estimation with active learning to infer the posterior distribution of spatially-flat $\Lambda$CDM cosmological parameters from 18,000 realizations. The results yield a marginalized mean of the growth of structure parameter $S_S = 0.731 \pm 0.033$ (68\%). The forward model fits the data well with a probability-to-exceed of 0.42, and the constraints are wider compared to a Gaussian likelihood analysis due to cosmology dependence in the covariance. Neglecting variable depth and anisotropies in the point spread function can lead to an overestimation of $S_S$ by about 5\%. The findings are consistent with previous analyses of KiDS-1000 and highlight a 2.9$\sigma$ tension with early-Universe constraints from cosmic microwave background measurements. The work underscores the importance of forward-modelling systematic effects in upcoming galaxy surveys like *Euclid*, *Rubin*, and *Roman*.