It is interesting that you are apparently attempting to equate the concept of ‘ātman’ with the word ‘soul’
However they are two different concepts. A soul, in the popular Western sense of it, is an embodied spirit that people supposedly have in them (so it makes sense to speak about whether I have a soul, I dont have a soul etc). This implicitly means thay the soul and the person who has them are two different concepts, so it makes sense to argue if the former has (or conceptually can possibly have, or not have) the latter.
Ātman (Pāli attan), on the other hand isn’t what a person can have (or not have), it is not about having at all. It is that which a sentient person cannot not be i.e. themselves.
It is that without which a sentient being wont be able to call themselves “I” or “me” or “my” i.e. the core of their own self-identity i.e. their self-identifiable personhood.
For someone to not be ātman i.e. themselves (observe the word “be”, not “have”) means to not recognize any self-identity, which means the Buddha doesnt view himself as himself i.e. he doesnt consider himself a Buddha or have any other form of identifiableness or characteristics or attribute that would differentiate him from anyone else. In fact that would mean he denies his own identity to himself. That would be a hopeless illogical catch-22 conceptual mess.
So when early Buddhism says the physical body’s skandhas are anātman, it is saying that the body or its skandhas is not who you are… they are not your self.
It is not saying ‘you are not youself’ (i e. ‘you are not ātman’) because that would be meaningless.
What the Buddha was advising - is to not have attadiṭṭhi (Sanskrit: ātmadṛṣṭi) i.e. to theorize about what the ātman is or is not (because practically everyone who theorize are theorizing from their ignorance, and in their ignorance they are superimposing aspects of the external world i.e. anātman - on themselves i.e. ātman - conceptually). So theorizing leads not to knowledge but to the propagation of ignorance and unnecessary mental-stress and pointless fatigue.
He was asking his followers to abandon theorizing about the nature and origin of their core identities, and to cease identifying/equating their-self identity with anything else. So when he says everything that can be grasped with the five senses is anātman, he means that you cannot grasp your self-identity with your senses, and anything which you can so grasp isn’t your self-identity.
He was not asking them to not believe in the idea of themselves (i.e. to disbelieve the concept ātmatva or self-identity).