Godot has been running on Oculus Quest since early 2019 with improvements made throughout the year. To help developers with this integration, the Godot team has posted a tutorial walkthrough for Oculus Quest development with Godot from start to finish.

You'll need Godot 3.2 or later (currently in beta) along with the export templates and the Oculus Quest plugin. Learn more from the tutorial itself at https://godotengine.org/article/godot-oculus-quest-support.