I am working on a problem where I try to predict the onset of a reaction (of participants), given a set of time-series signals. I know that the event always happened, it is just a matter of question when exactly it happens. The goal is, later on, to predict in real-time whether or when the event would happen, given current (measured) inputs to the model. I see two different ways to approach it: A) as a "classification" problem to predict whether the event would happen or not, at a given time with the current inputs, or B) as a "regression" problem to directly predict the time of the event onset. (I probably did not use those terms correctly in this context but at least to me, those approaches sound like they have the main goal of classification and regression methods, respectively.)
Approach A should output a probability of whether the event would happen or not, and I can think of survival (time-dependent cox), or logistic regression. This approach may, apart from the mean predicted probability, also deliver confidence/prediction intervals of the probability, given current inputs to the model.
Approach B should be done in a probabilistic way to get the full pdf of the predicted onset time, e.g. with a Bayesian regression model (using stan, brms, PyMC3, etc.). Then, by constructing the cdf of the predicted onset time (given current inputs to the model), I could get a similar (?) probability of event onset as in approach A.
My question(s): Which approach sounds favorable for my kind of problem, or could either of them work? Could I compare both with a common evaluation metric like AUC?
My current thinking: I feel like approach B could deliver richer information (the time itself and a probability), and it might be more straightforward to evaluate (e.g., via RMSE). But when looking at previous research, it suggests going for approach A (many medical studies have done it that way, at least).
Edit-1: The starting point is defined as when the participants enter a particular phase of the experiment. All covariates are changing over time and are continuous, except for one that I would like to keep in an interaction, as a boolean variable. All covariates are time-series signals that are not random, rather smooth/slowly changing, continuous, and sampled at 100 Hz.