They used a Quantum Computer powered by Tesla to reverse engineer the Private Key of course.
FBI, NSA, CIA, DHS actually is working on something technical like Quantum computing, but going down that direction would be wishful thinking on my part.
FBI did not obtain the private keys. Instead, they took legal action against an exchange or some kind of custodial wallet that has server in Northern California (Hint: Coinbase). Those idiot "hackers" were grossly incompetent!
It is quite possible that half of the "hacking team" were incompetent. I've been reading that the ransomware creators will partner with anyone with access to a business like this one, and split the ransom. Since it was about half the ransom recovered, it would not surprise me if this was the half of some dope within the company trying to make a quick couple million.