The largest number (finite) level here are maybe the TREE levels. And yes TREE is considered a number, a gigantic number which is unaccountable by you and me.
There even larger numbers that go real large than TREE, but haven't gotten into the backrooms yet. The largest one being "Rayo's number" a number so large that it'll take the entirety of many universe eras from big bang to nothing in a cycle to finish the number if you were to count it.
I was gonna make level rayo, but I lost interest of making it since it felt uncreative.