If AGI were invented tomorrow, it'd probably be by open AI. I doubt whoever made it would tell anybody, because the government might step in, they certainly wouldn't make it freely available online.

If it was about as smart as a person, they'd probably roll out a weak "agent" version of for demo sake to get more funding. This would continue until they made one that was significantly more intelligent or cheap.

If they had one that was very cheap, they'd have 10,000 agents of it act together as a group to try to emulate a smart one, by considering every angle of every problem. This would likely mean 10,000 engineers making the AI better/cheaper/faster.

If they had one that was far smarter than a human, they probably have it improve itself, making it far better/cheaper/faster.

Then they'd try to see if they could use it to change the world. They'd have thousands of thinking machines that could be online, place phone-calls, engineer things, create ideas, make political campaigns, dig up dirt on people, or who knows what.

No "country" would "win," because this isn't a team sport and countries are just lines on maps.