You can try to use a partial GET (byte range) to seek around the file to find its end by trial (and avoid downloading 20GB), but I'm pretty sure 99% of the resources supporting a partial GET will also report a Content-Length in the header.

Short answer: no, AFAIK

Update:Here's what I found in the standard. I don't quite understand the verbiage, but take a look at this.

In reply to Re: Determining Content-Length when there is no Content-Length header by calin
in thread Determining Content-Length when there is no Content-Length header by hacker

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