Chances are when you submit a report to police, government and they help you to find the scammers.
Sometimes you will see white hat hackers stole funds and refund it to projects. I am not sure they are really hack cases or just manipulating ones.
What are the chances? Substantially slim that the government can do anything, then the process to go about it would be something else, because you will have to prove that the funds were
in truth, stolen. I can imagine losing $300 worth of bitcoin and going to my local police station to make a complain, i doubt if i will be taken too seriously.
The government can't even do anything, unless there is an address on a centralized exchange that links to the thief, then the government will have to authorize the exchange to provide more info about the thief, what a heck of a process, and i can guess you will have to lose a very large sum of money for the government to do this.