Theoretically, let's say you have a brand new laptop that is fully functional but has no built-in browser. (You also don't have a phone or any other separate device.) How would you download a web browser without being able to see the web?
Most of the curl/powershell answers assume you know the URL to download it from, which might not be correct since they are usually long and not easy to memorize.
However, considering the scenario on the question, I would assume that browser vendors would create very easy-to-remember URLs so you could get their browser without having to memorize 100-character-long URL e.g. mozilla.org/firefox.[exe,bin,sh,deb]
I agree, that the browser vendors should do this for this purpose. Perhaps also add a file "downloads.txt" which explains them so that you will know which file to download (even if the file you want to download isn't a web browser).
Keep a liveboot USB handy with OS that has a browser. Boot with it.
Save a few installers for common browsers on a USB/SDC/local NAS etc.
If your on *nix, wget/curl/ftp/scp/sftp the files from a known location.
You can do the same in Windows in powershell or CMD
Getting BitTorrent installed seems like it would be a challenge. FTP seems possible as most OSes preinstall it, but what FTP server has a browser installer and how would you find it?