When a level is published, it gets into the Queue of "new" levels. Those are the levels that will be shown on the Gem levels in the sky, (AKA "Good or Bad" levels). The queue will normally give the new levels to testers in about 2 days, depending on how long the queue is, how often levels are being published (currently we get a new level every 15 seconds), and how many players are playing the Gem levels.
Once the level is next in the queue, the level enters the second system. The Testing system will try to select representative players to test something in particular; like the CC's requirement for playing and finishing a level (this dictates the CC range), how many tries it takes (this checks for difficulty) and finally Likes vs Dislikes. For the CC range, it will gradually send the level to slightly higher and slightly lower CC range players until it finds the spot where players are unable to finish. Actually most levels get the whole range open for all players.
The next system will determine if a level is good or bad. There are a few conditions that will set a level as "Not apt for the path". For example if the creators spent next to no time on the creation of the level (trying to iron out the flat levels), or if the level got tons of dislikes (people just don't like it).
The normal thing that will happen is that the level will be marked as "Public", this means that it got enough likes to go into the general level population. This is where the vast majority of levels are kept.
Lastly, our Featuring system is the one that actually looks for the best levels (hopefully, and in most cases, it does work properly). From the 6+ million levels published, our priority is to show the most liked and the most relevant. So we look for the newest levels coming fresh out of the "Good or Bad" and check which of them are public. From the thousands that just came out, we look for the one that got the highest percentage of Likes vs Dislikes. Because there are just so many levels, basically they all compete against each other for the spot.
Once selected, they go on the list of levels for the path to be awarded to players. So when players open their latest chest on the path, the game sends them the next 5 levels on the list.
Sometimes players see levels that have a high Dislike percentage on the path. This usually means that the level did very well coming out of the Good or Bad levels, but after being shown to the Adventurers, they didn't like it much and started Disliking it. It is then removed from the list and the next level with the higher percentage of Likes is chosen to be put on the list instead. However since the level had already been loaded in the pack of 5 levels, a certain amount of players already have it and need to play it before they get the next top levels. That is why they see that it has a lot of Dislikes.
Basically we teach the game how to do this, because it adapts all the time to what is coming at it. It would be impossible for us to go level by level selecting them by hand. That is why the Likes and Dislikes are so important for us, players help us curate the levels.