There are countermeasures you can take against timing attacks, pattern analysis, and other capabilities an attacker may have if they control many relays. If you're trying to exfiltrate military secrets to the Russians, you can probably do it, but you'll have to be extremely careful. Your behaviour is as important as the network you use to communicate over, if not more important.
There is no single state actor that has access to all data centers in the EU, though. For some countries, there's barely a state actor that can access all data centers within a single country.
There is no tool that will let you become immune against a theoretical hyper powerful super government that controls all data centers, just by clicking a button. There never will be.
There's some neat math that shows how one could send (radio) signals which are undetectable to an observer. Last I read, the research was in specific, purely theoretical scenarios but the idea is that you could send bit impulses which stay within the noise floor. Transmit with a power less than R^2 (in discrete time and ignoring triangulation and you have to pre-coordinate the timing of the transmissions with your partner via pre-shared one time pad and use plenty of error correction) the enemy observer cannot prove that someone is sending signals at all.
Maybe no such techniques could ever apply to the internet, but I'm not sure it's proven impossible. You would need a well defined threat model but if you can show that your enemy is working with noisy data and strictly in the digital space, I don't see why statistical de-anonymization couldn't be foiled.
This FUD comes up whenever Tor is mentioned on Hacker News. The answer is: let's say you think Tor isn't 100% flawless. What are you going to do? Not use Tor? It's better than any other option.
What you'd do is that you'd write a distributed remailer where fixed-size messages are sent on fixed timeslots, possibly with some noise in when it's transmitted, with a message always being sent on its timeslot, even if a dummy message must be sent.
I've been writing a system like this in Erlang, intended to be short enough that you can take a picture of the source code and then type it in by hand in a reasonable amount of time, as a sort of protest against Chat Control. I'm not sure I'm going to release it-- after all, they haven't passed it yet, and there are all sorts of problems that this thing could needlessly accelerate, but I've started fiddling with it more intensively recently.
Ah. It actually looks very sensible. I knew things like that existed, but didn't know they had dummy messages.
I guess my approach is more P2P, more simplicity, shortness and clarity focused, as well as perhaps emphasizing general networking less-- I sacrifice more, I'm fine with 3-6 second delays on all messages, for example. I guess I also emphasize scale in that I intend to have 10,000+ connection open simultaneously on every peer, and because of this you don't even always need the retransmission aspect, since the person you want to talk to might be in the group of 10,000 that you send a message to every second.
So in my thing the mixing is less important and the retransmission aspect is only needed when the network grows so big that you, when you connect don't happen to randomly end up directly peering with the person you want to talk to.
While there aren't as many services available, there are alternatives to Tor. Veilid on the protocol level seems to be quite promising, and I2P and other networks also provide some Tor-like features.
If you're trying to browse the web then you won't find many alternatives, but if you're looking to avoid the authorities doing some data exchange, you have options.
