The quote “Aham Brahmasmi” can be understood following spirituality as in Bhagavad Gita.
Can anyone say, ‘I am Brahman”? This would be a wrong quote, a misinterpretation of spiritual teachings contained in Bhagavad Gita and also Upanishads (independent spiritual treatises).
Spiritually speaking human beings could never say anything because they had no entity in the world of souls’ atmans except being a medium for souls’ atmans within.
But as a soul atman, a spiritual traveler we can definitely say “I am part of Brahman” never ‘I am Brahman”. The summation “I am part of Brahman” comes from the analogy that we are primarily a spiritual traveler, a cosmic traveler, a spirit, consciousness manifesting human form.
We as a soul atman were part of Brahman. If an individual grain of sand is an independent soul atman, the whole mound Brahman, God Almighty. If an individual piece of puzzle is an independent soul atman, the completed puzzle Brahman, God Almighty. God Almighty is called Brahman in Hinduism.
As a spirit we were not distinct from Brahman in essence.
When big bang occurred we as an independent pure spirit, soul atman separated from its source Brahman himself. And when human beings indulging in spirituality succeed reaching state of enlightenment and finally moksha salvation, we again merged back with Brahman similar as a piece of puzzle takes its right place in the full puzzle. For a pure soul atman there was nothing more to do than rejoin the source from where it emanated.
The puzzle gets completed; Brahman God Almighty regains its original primordial form only when complete dissolution of cosmos (called Pralaya in Hinduism) occurs. It is at this moment all individual pieces of puzzle combine together to become the completed puzzle which is none other than Brahman, God Almighty himself.
Seekers, travelers of spiritual path could always say we were part of Brahman but never, I am Brahman.