The evolution of the atomic structure of LaAlO_{3} grown on SrTiO_{3} was investigated using surface x-ray diffraction in conjunction with model-independent, phase-retrieval algorithms between two and five monolayers film thickness. A depolarizing buckling is observed between cation and oxygen positions in response to the electric field of polar LaAlO_{3}, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. Based on these structures, the threshold for formation of a two-dimensional electron system at a film thickness of 4 monolayers is quantitatively explained. The findings are also qualitatively reproduced by density-functional-theory calculations.