I work with learning and predicting events (of various kinds) in time and space. The data is completely observable without censoring. Even so, survival analysis is a useful tool to learn a distribution over time and sample from it to predict future events (deaths). A potential challenge is the inclusion of time-varying covariates in the model. While the Cox's regression model can easily accommodate such covariates, predicting survival times is not easy due to the implicit assumption of treating the baseline hazard as unimportant (unspecified). On the other hand, the inclusion of time-varying covariates is not straight forward in the parametric models.
What is the best way to go about this? Given that the data lacks censoring but includes time varying covariates, is there another tool that is better suited to handle such a problem?