If you have a target variable, and other input features, you can treat this problem as a normal regression problem. Using model like linear regression, Random Forest Regression, or XGBoost is very straight forward from there

You can then look at feature importance to try to weed-out the uncorrelated features (if you want to). There are a few automated ml for timeseries, but currently I mostly use Pycaret

But if you suspect that your target variable autocorrelate, model like SARIMAX can be used instead. An automated version of that is Statsforecast e.g. AutoARIMA with exogenous variables (haven't used it though)

But noted that if you are in direct control of a few variables, and you want to predict want will happen, this is no longer a simple regression anymore i.e. the data distribution may shift. That would be in Casual Inference territory (see this handbook)