Whether we like it or not I think we have to deal with anatta on almost every step of the way. Simply because ‘progress’ means to shed another layer of ‘skin’, at least temporarily.
The big distinction is the delusion of complete anatta, and a gradual experiential anatta. Plenty of people are just parroting “there is no atta, there is no atta”, as if repeating a sentence makes it magically true. If one says that one is either enlightened, or one is fantasizing.
Take just the first jhana for example. If you want to realize it you have to have a distance to ‘kama’ (sensual desire) and the hindrances. But these are not just words, they are part of the very fabric of ourselves. If we can pause them for a while we have distanced ourselves from a part of ourselves - that’s what I mean with gradual anatta.
Towards the second jhana we even have to distance ourselves from the movements of the mind (thoughts, pressure, micromovements) so that samadhi and unification can take place. But again, ‘the movements of the mind’ are not just words, they belong for most people to the core of their subjectivity. So if I manage to pause that I truly practiced another deeper layer of anatta, etc.
All the way the ‘full/complete anatta’ is just a fantasy. I have to work with whatever is available to me to distance ‘myself’ from it, and on to the next level, etc. Maybe at some point there is a reality of a ‘last layer’, but that is indeed not accessible to me anyway, and while conceptually interesting it should concern me not as philosophy/fantasy but as a surmountable mountain.