Actually we are the best prove that you can be the same and changing in the same time. Like, you go and read a diary you wrote 30 years ago. You don't reckon those pages were written by another person. Or if someone steal from you money you earned a month ago, you won't say ^I don't bother that money was not mine. So, all this idea of Self, is based on bad trasnlation and ignorance of what the conventional indian rules of philophy dictate thousand yeras ago. They use to define clearly something, before deciding to denie it existence or not. So, the Atman, was defined as an unchanging beyond time intelligent entity, not touched by Samsara. Atman was Amata also, immortal, and Nirguna, without qualities, and so on.
The Sadhu want to see this, with Yoga. Buddha was a Great Yogi, He went in to the forest and Meditate for years. Then He tried to teach the Immortal. In the sutta is written He said: now the gates of the Immortal are opened,
from Aryapariyesanā Sutta
apārutā tesaṃ amatassa dvārā
ye sotavanto pamuñcantu saddhaṃ
vihiṃsasañntilde;ī pagunaṃ na bhāsiṃ
dhammaṃ paṇītaṃ manujesu brahme ti
or from Mahāvastu
apāvṛtaṃ me amṛtasya dvāraṃ brahmeti bhagavantaṃ ye śrotukāmā śraddhāṃ pramuṃcantu viheṭhasaṃjñāṃ
viheṭhasamjño praguṇo abhūṣidharmo aśuddho magadeṣu pūvaṃ