The kagome superconductors KV3Sb5, RbV3Sb5, and CsV3Sb5 are known to display charge density wave (CDW) order which impacts the topological characteristics of their electronic structure. Details of their structural ground states and how they evolve with temperature are revealed here using single crystal x-ray crystallographic refinements as a function of temperature, carried out with synchrotron radiation. The compounds KV3Sb5 and RbV3Sb5 present 2×2×2 superstructures in the Fmmm space group with a staggered trihexagonal deformation of vanadium layers. CsV3Sb5 displays more complex structural evolution, whose details have been unravelled by applying machine learning methods to the scattering data. Upon cooling through the CDW transition, CsV3Sb5 displays a staged progression of ordering from a 2×2×1 supercell and a 2×2×2 supercell into a final 2×2×4 supercell that persists to T=11 K and exhibits an average structure where vanadium layers display both trihexagonal and Star of David patterns of deformations. Diffraction from CsV3Sb5 under pulsed magnetic fields up to μ0H=28 T suggest the real component of the CDW state is insensitive to external magnetic fields. © 2023 American Physical Society.