It depends on what kind of survival model you use and what you mean by "using just the coefficients from the model". You may need to integrate the instantaneous hazard to get the cumulative hazard, but that should be straightforward given that your time periods are equal and I assume you know the value of covariates for the all relevant times (if you do not have a full history for the individual you are trying to predict, then I cannot see how you would calculate cumulative hazards). So assuming you have the full history for the individual in question, the question becomes if you know the instantaneous hazard for all times.
If you have a parametric survival model (e.g. a Weibull proportional hazards model), having the parameters for the baseline (e.g. scale, shape) and the covariates (regression coefficients) is sufficient to calculate everything you want. Since you said that you have time-varying covariates, I suspect that you have a semi-parametric model, such as a Cox proportional hazards model, thus getting the baseline hazard out is slightly more work, but perfectly doable. It is my understanding that using the standard Cox model with time-varying covariates allows you to continue to use all the standard methods with it, so there should be no problem that methods do not work as expected. There is some discussion of getting the hazard out of a Cox model here: Cox baseline hazard
If you can give me a reproducible example of what kind of model you want, I can check and attempt to give you a code example.