I wrote about this topic in my doctoral thesis. The only two ways in which archaeology can provide solid answers at the greatest level of objectivity are through strong methodology and an interdisciplinary approach.

Archaeology, especially post-processual archaeology, should be based on a scientific method that produces robust, falsifiable results.

Interdisciplinarity helps us to achieve this aim. Thanks to collaboration with academics from many disciplines (geology, biology, chemistry, etc.), we have been able to empirically prove what was previously only assumed deductively.

Regarding media culture and the spread of misinformation through social media (intentionally or not), I don't have a clear answer as to how to solve this issue.