The Hooded Champion ranger gets Favored Enemy at 5th level, starting with a +2 bonus.
The rules for class archetypes explain that if an archetype replaces part of a sequence of features (including Favored Enemy), then the sequence is effectively delayed by that many upgrades.
If an archetype replaces a class feature that is part of a series of improvements or additions to a base ability (such as a fighter’s weapon training or a ranger’s favored enemy), the next time the character would gain that ability, it counts as the lower-level ability that was replaced by the archetype. In effect, all abilities in that series are delayed until the next time the class improves that ability.
In this case, the Hooded Champion skips the 1st level Favored Enemy feature.
This ability replaces favored enemy at 1st level.
As written, they only lose the 1st level feature, but don’t lose the other Favored Enemy features at later levels. Therefore at 5th level, they gain Favored Enemy for the first time, so it counts as the lower level (1st level) version and grants a +2 bonus.
At 10th level, the Hooded Champion gets the next lower level (5th level) version of Favored Enemy. Their bonus against their original favored enemy increases to +4, and they gain a second favored enemy with a +2 bonus.
This continues for every successive upgrade. At 15th level, the Hooded Champion gets the 10th level version of Favored Enemy. And at 20th level, they get the 15th level version of Favored Enemy.