Jessica,
If you have remote access to the server, the easiest is to download the libraries and put them on the server in the windows temp folder.
If you want to allow the server to download the binaries automatically, it needs to have a connection to the internet and more specifically to om https://storage.googleapis.com/chromium-browser-snapshots/Win_x64. If the connection is not open, then the network team will have to add a firewall rule to allow the connection. Or let it pass via the proxy.
Also make sure the site properties are set correctly. If you put binaries on the server yourselves, the site propertie for the version must have to number of the binarie you downloaded.
You also might want to check if the IIS_IUSRS has access to c:\windows\temp.
Does this help you further?