I have found a ton of examples online like this:
WebRequest webRequest = WebRequest.Create(stagingFileMap.URL);
webRequest.Method = "HEAD";
var webResponse = webRequest.GetResponse();
string fileSize = webResponse.Headers.Get("Content-Length");
double fileSizeInBytes = Math.Round(System.Convert.ToDouble(fileSize), 2); // yadda yadda
This is great, except WebRequest is obsolete / deprecated. I cannot find a good example that shows how to do it using HttpClient (maybe you can't use HttpClient, I don't know).