I would like to determine which predictors most strongly influence my outcome variable accounting for repeated measures of the two timepoints.

A factor analysis was suggested to me (as the first and final step for my purposes), yet this will not be related to my dependent variable in any way, to my understanding. Is it ever the case where I could do a FA, then use the independent predictor variables that made it into the first factor loading in a regression? I’m sure this introduces bias given the dependent variable wasn’t considered in the FA?

Otherwise, perhaps a penalized lasso or elastic net regression or random forest would be an improved approach here? But also to my understanding, these may not be able to account for repeated measures. In this case, is it possible or even recommended to conduct a lasso/elastic net/RF on each timepoint separately, then choose the common predictors between the timepoints to include in my second step (regression)?

Is there another statistical approach you would take here? Many thanks!