IIRC, within the FBI’s jurisdiction and international don't go together. Isn't the FBI restricted to operating nationally only?
But to answer your question more fully, you can't solve this problem without supranational cooperation. A "police force" working to safeguard the Internet would have to work under authority of the UN, not any single nation.
The UN isn't a government; it has no real legal authority (international 'law' is something different), no law enforcement. It has no legitimacy - who elected them?
It's an association of governments, where they get together and organize things. All the power is in the individual governments. There are some grey areas and exceptions, but overwhelmingly the above is the case.
The UN could coordinate cybercrime law and national agencies.
The U.S has an MLAT with Israel and routinely extradites. If the crime was committed on U.S. soil (intrusion, conspiracy), my understanding is that it is within U.S. jurisdiction.
But to answer your question more fully, you can't solve this problem without supranational cooperation. A "police force" working to safeguard the Internet would have to work under authority of the UN, not any single nation.