The Early Buddhist Texts (EBTs) do not claim that the ātman is ever-changing.
In fact the EBTs say the opposite i.e. Whatever is ever-changing cannot (according to the Buddha of the EBTs) be called ātman. So things that are ever-changing are called anātman (i.e. non-ātman).
What we (lay people or novices) might consider as defining ourselves (ātman) is either our physical body, or our feelings, or our conceptions, or our habits/practices, or our consciousness. The Buddha (according to the EBTs) says these skandhas arose at a point in time and are all perishable at a different point in time i.e. they are not the ātman (they are anātman) – so clinging to them thinking they are me/mine leads to duḥkha eventually.
From the MN147:
Taṁ kiṁ maññasi, rāhula, cakkhu niccaṁ vā aniccaṁ vā”ti?
What do you think Rāhula, is eyesight/vision everlasting or not?
“Aniccaṁ, bhante”.
Not everlasting, sir
“Yaṁ panāniccaṁ dukkhaṁ vā taṁ sukhaṁ vā”ti?
Whatever that’s not everlasting - would it be dukkha or sukha?
“Dukkhaṁ, bhante”.
Dukkha, sir
“Yaṁ panāniccaṁ dukkhaṁ vipariṇāmadhammaṁ, kallaṁ nu taṁ samanupassituṁ: ‘etaṁ mama, esohamasmi, eso me attā’”ti?
Whatever that is not everlasting, is dukkha and is liable to change - is it proper to consider such a thing as “this is mine, I am this, this is my self”?
“No hetaṁ, bhante”.
No indeed, sir.
So we see that whatever that is duḥkha/dukkha, anitya/anicca & anātman/anattā are not fit to be considered to be oneself (ātman/attā).