Is it possible without someone who has industry experience and connections with networks?
For example PlutoTV has CBSN and some CNN/NBC news channels, though it appears not to be the standard feed from MSNBC or CNN 24/7, but just looped feeds...
Content is a whole nother animal. Pluto TV is a Viacom product and spends millions on licensing those shows (which, yes, are looped). You could show free films or public domain content on your private channel (and many people do), but getting licensed media will require buying the license from whoever owns the productions.