  The last few years have seen the development of a promising theoretical
framework for statistics of the cosmic large-scale structure -- the theory of
large deviations (LDT) for modelling weak-lensing one-point statistics in the
mildly non-linear regime. The goal of this series of papers is to make the leap
and lay out the steps to perform an actual data analysis with this theoretical
tool. Building upon the LDT framework, in this work (Paper I) we demonstrate
how to accurately model the Probability Distribution Function (PDF) of a
reconstructed Kaiser-Squires convergence field under a realistic mask, that of
the third data release of the Dark Energy Survey (DES). We also present how
weak lensing systematics and higher-order lensing corrections due to intrinsic
alignments, shear biases, photo-$z$ errors and baryonic feedback can be
incorporated in the modelling of the reconstructed convergence PDF. In an
upcoming work (Paper II) we will then demonstrate the robustness of our
modelling through simulated likelihood analyses, the final step required before
applying our method to actual data.
