The next technological breakthrough in millimeter-submillimeter astronomy is 3D imaging spectrometry with wide instantaneous spectral bandwidths and wide fields of view. The total optimization of the focal-plane instrument, the telescope, the observing strategy, and the signal-processing software must enable efficient removal of foreground emission from the Earth's atmosphere, which is time-dependent and highly nonlinear in frequency. Here we present TiEMPO: Time-dependent End-To-end Model for Post-process Optimization of the DESHIMA spectrometer. TiEMPO utilizes a dynamical model of the atmosphere and parametrized models of the astronomical source, the telescope, the instrument, and the detector. The output of TiEMPO is a timestream of sky brightness temperature and detected power, which can be analyzed by standard signal-processing software. We first compare TiEMPO simulations with an on-sky measurement by the wideband DESHIMA spectrometer, and find good agreement in the noise power spectral density and sensitivity. We then use TiEMPO to simulate the detection of the line emission spectrum of a high-redshift galaxy using the DESHIMA 2.0 spectrometer in development. The TiEMPO model is open source. Its modular and parametrized design enables users to adapt it to design and optimize the end-To-end performance of spectroscopic and photometric instruments on existing and future telescopes. @en