Based on spending much of the last week looking at the list of available servers myself and based on what others have posted, it looks like the restrictions are population based and so come and go throughout the day - e.g at peak times in both NA and EU all servers are locked to new characters, but as populations fall these are lifted on most servers.

But there seems to be a small group of servers where these restrictions never lift - at the moment this is the case for Moogle (EU), Ultros (NA) , Behemoth (NA), Cactuar (NA), Excalibur (NA) and Hyperion (NA). The only time in the last 4-5 days that I've seen these servers available was just after the downtime on Wednesday, when I guess that the populations were briefly low enough that the restrictions didn't kick in for a short time.