Assuming money is not an issue and the only thing that mattered is a completely self reliant connection to the wide web.
www.nycmesh.net/
If You just want a rock solid reliable means of communication and privacy is not an issue, look into Morse Code on Amateur Radio or CW mode. I am 100% positive that if You managed to learn it and make contact with any HAM, they would happily forward your personal message for free.
if You are just looking for an untraceable connection, buy a SBC with cash from a local electronics store and find an open wifi connection. Just be sure to bin the SBC when You are done or learn about MAC spoofing at the very least.
If You are looking for a more permanent solution and are not overly concerned with the connection being traced back to Your geo location, but still want privacy. You could look into starting a numbered company then purchasing a StarLink system through it.
There may also be a few AmSats that offer connections but they would have extremely slow speeds.
The most independent way to connect IMHO, is to connect through a peering point/internet exchange, but you need to contract for physical space, for IP space, for connection to the peering point, and for connections with each other network you connect to there. So, you end up with lots of involvement, but you can also pick from many transit providers, and maybe peer directly with other networks (depending on their policies)
Edit to add: the thing about the internet is there is no 'the internet' to connect to, you're connecting (mostly transitively) to every other network (ideally), many of which are government or commercial networks.
Connecting to other continents requires fiber strung under the oceans, or a more bandwidth constrained path through satellites, or a very, very slow radio link (which must be government licensed)
Governments are very picky about entities that cross their borders.
To reach the traditional internet, you'll need someone else to provide a tunnel. But if your target also has a node in these networks you can communicate just fine.