It looks like window.open will take a Data URI as the location parameter.
So you can open it like this from the question: Opening PDF String in new window with javascript:
window.open("data:application/pdf;base64, " + base64EncodedPDF);
Here's an runnable example in plunker, and sample pdf file that's already base64 encoded.
Then on the server, you can convert the byte array to base64 encoding like this:
string fileName = @"C:\TEMP\TEST.pdf";
byte[] pdfByteArray = System.IO.File.ReadAllBytes(fileName);
string base64EncodedPDF = System.Convert.ToBase64String(pdfByteArray);
NOTE: This seems difficult to implement in IE because the URL length is prohibitively small for sending an entire PDF.