It isn't 100% clear what the question is, but it seems like the desired outcome with anything like this is to access the results from the SOQL query.
All the results, with the exception of the ID field, will be in the anyElement response.
Something like SOAP UI can make it much easier to see what is going on here. E.g.
It looks like you want to target the "ListSubscriber" Object where the CreateDate is a recent value (greaterThan %%date%%).
Assuming only "Active" subscribers are being added to your All Subscribers List only, you can use the simple filter below:
Wsdl2Apex should be handling this conversion for you. Typically the only way to get the raw response that you have is to do a System.debug(calloutResponse); on the web service response objects. E.g. If the debug output includes members with the _type_info suffix then you are dealing with the WSDL2Apex generated stub classes.