Ecology has been surprisingly slow to address the uncertainty and bias that results from using short-term time series to draw long-term inference. To improve our understanding of assumptions around the temporal structure of vital rates (e.g., survival, reproduction), we need tools that are feasible and capture longer-term, state-structured population dynamics. Here, we use inverse modelling of a set of integral projection models (IPMs) to show how demographic rates can be accurately reconstructed from state-structure fluctuations in a population time-series. We use a particle-filtering optimisation algorithm to fit vital rates from time-series of varying length, parameter combinations, priors, and life histories. We show how key life history traits such as generation time have little effect on the ability of our approach to accurately identify vital rates using state structure over time. Further, contrary to our expectations, the duration of our time-series data has relatively modest impact on the estimation of vital rates compared to the critical role of prior knowledge on vital rates. Our framework to estimate IPM vital rates highlights the potential of inverse models to extend time-series for demographic models, but also demonstrates that long-term time-series are not a perfect surrogate for detailed demographic inference. We discuss the need for more work exploring the conditions when inverse modelling is an adequate tool based on species traits.