That will probably work about as well as the proposal to put a data center on Sealand [1]. Or Cryptoland. Or Satoshi Island. Or Blueseed.[2]
Or the Space Kingdom of Asgardia, which launched a successful satellite with some data storage in 2017.[3] That lasted until 2022, when the satellite re-entered.
[1] https://en.wikipedia.org/wiki/Principality_of_Sealand
The people who originally sent the thing up, can give up their access.
As long as you don't have to physically touch the thing again, you can use some clever cryptography, so that no one is technically running it.
That's easiest, if you just let no one have any privileged access. But you can use (public key) cryptography or similar to give some anonymous people on earth access. Or, for peek publicity value, the data centre can give access to whoever holds a specific bitcoin.
You can really trade it as a token on some blockchain, and the data centre itself can read the chain (as long as someone sends it to them, but anyone can do that).
The data centre will do the bidding of whoever has the private key that's associated with that specific token on the blockchain.
But the whole blockchain bit isn't even necessary: some anonymous person on earth can hold the private key. When they want to pass on the rights to the datacentre, they send it a command (signed with their own private key) to obey some other key in the future.
Governments can't figure out who holds the relevant key. (At least not in theory. In practice, they can try to do classic spy craft and meta data analysis etc.)
So even though the owner of the key might sit in Germany or the US or Switzerland, those countries don't know that.