One of the goals of control charts is to aggregate information from a complex process into one or more univariate summary statistics. Depending on the process type (stationary, non-stationary etc) and the dimensionality of the process, different control charts can be used. This might suit you well - especially since you considered distances already.
Two simple control chart approaches to consider are the MEWMA and MCUSUM control charts. These methods are implmented in the MSQC package in R. Analytical procedures for these are implemented in the spc package in R.
Montgomery's Introduction to Statistical Process Control provides implementation details, in clear, non-esoteric wording in case you would like to know more.
Both charts will work well if you don't have too many variables (since they require the inversion of a covariance matrix, which can become problematic if variables are highly correlated), and can handle some level of non-stationarity.
To use these methods, you must first train a model on data without faults (this may be no problem for you - perhaps you have none). This means you should select a value of the forgetting factor (MEWMA) or the reference value parameters (MCUSUM) based on a test set if possible. This can be done by cross-validation, or eye-balling it if you are in a rush and this is mostly for data exploratory purposes.
Once you have the parameters of the control charts, you can apply them "in the wild". This will return to you a univariate control chart statistic summarizing the information from your time series, as well as control limits indicating when your process is behaving atypically.