That's not necessarily the hard part. I mean, it's hard, but it's not
the hard part.
We know this because what this game is trying to do is done already a long time ago. It's a description of the original vision for Second Life. In fact Second Life was explicitly an attempt to create "the metaverse", with all user-generated content. Linden Labs used to write about the challenges they faced in making that vision real so we have a good idea of where the challenges really lie, or at least did 10-15 years ago.
First problem: physics. LL sharded their world, which was indeed infinite. The problem is each shard required its own dedicated high end server, which made "land" extremely expensive. Amazingly, people bought it anyway, LL developed a small but extremely rich customer base who were willing to literally rent high end (what would be today) cloud VMs just to have a very small space to call their own online. For a brief period it was also trendy for companies to open up spaces in Second Life.
The reason land was so expensive was that physics (collision detection and movement, mostly) required the server to constantly iterate every object within the zone and the calculations scaled with number of objects. Shutting down physics when nobody was there also wasn't possible because the metaverse concept implied allowing arbitrary scripting, and scripts frequently expected the world to keep running even if nobody was there. The answer in SL to "if a tree falls and nobody is around to hear it, does it make a sound" was a resounding yes.
The second big problem they faced was that user generated 3D content was extremely un-optimized. The biggest complaint users had about SL was always performance. Eventually they gave up promising to improve it and came clean with the userbase: SL was slow and always would be because users kept making slow content. In particular SL was set mostly outdoors, and even when indoors, people loved doing things like creating semi-transparent windows. The ability for any object to change at any moment (users created content in-game) also implied they couldn't use all the "baking" techniques professional games use to optimize rendering. So the rendering algorithms had to be very primitive, and there was lots of overdraw, so SL really chugged even when drawing scenes that looked very basic compared to what high end games could do. And of course hobbyist metaverse users are not pro grade 3D artists so they tended to make a lot of ugly stuff anyway.
So syncing player data was certainly a sub-challenge, but compared to the difficulties posed by cost effective sharded physics and totally un-optimizable 3D scenes, it wasn't that big a deal.