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The kagome superconductor family AV_{3}Sb_{5} (A=Cs, K, Rb) emerged as an exciting platform to study exotic Fermi surface instabilities. Here, we use spectroscopic-imaging scanning tunneling microscopy (SI-STM) and angle-resolved photoemission spectroscopy (ARPES) to reveal how the surprising cascade of higher- and lower-dimensional density waves in CsV_{3}Sb_{5} is intimately tied to a set of small reconstructed Fermi pockets. ARPES measurements visualize the formation of these pockets generated by a 3D charge density wave transition. The pockets are connected by dispersive q^{*} wave vectors observed in Fourier transforms of STM differential conductance maps. As the additional 1D charge order emerges at a lower temperature, q^{*} wave vectors become substantially renormalized, signaling further reconstruction of the Fermi pockets. Remarkably, in the superconducting state, the superconducting gap modulations give rise to an in-plane Cooper pair density wave at the same q^{*} wave vectors. Our work demonstrates the intrinsic origin of the charge stripes and the pair density wave in CsV_{3}Sb_{5} and their relationship to the Fermi pockets. These experiments uncover a unique scenario of how Fermi pockets generated by a parent charge density wave state can provide a favorable platform for the emergence of additional density waves.