In Advaita Hindu philosophy, there is no essential difference between the living entity and Brahman. The word often translated as Lord in early texts referred to ‘turiya’, the fourth state. (
@Aupmanyav may correct or confirm this.) So someone may be saying God to refer to an irrefutable and ongoing experience, not at all at odds with science. And not at all like the God of the Bible.
BTW.....note to posters....Atheism is not ‘belief that there is no God’, it is the absence of a belief.
I agree to your last deposition that atheism means an absence of belief in God. Strong atheism goes beyond that in denying even the possibility of the existence of God, soul or ghosts. I am a strong atheist.
As for Advaita (non-duality in Hinduism), there are various shades. They range from:
1. Acceptance of existence of Ishwara (God) as a worldly truth but denial of that at the level of absolute truth, where it is only Brahman (Sankara's
Advaita),
2. Acceptance that living beings and Brahman are same but they have different attributes (Ramanuja's
Vishishta Advaita), Ramanuja says that Vishnu is the Brahman.
3. Acceptance that living beings and Brahman are the same but their relationship is indescribable (Chaitanya's
Acintya Bheda Abheda Advaita - Hare-Krishnas), Chaitanya says that Krishna is the Brahman,
4. Acceptance that living beings and Brahman are simultaneously same and different (Nimbarka's
Dvaita-Advaita), Nimbarka says that Krishna is the Brahman,
5. Acceptance that there is no real difference between living beings and Brahman, like sandalwood makes its presence felt through its scent even if sandalwood can't be seen (Vallabha's
Shuddha Advaita), Vallabha too says that Krishna is the Brahman.
My view goes beyond Sankara, i.e., "if Ishwara (God) is a truth only at the worldly level, and untruth at the absolute level, why accept its existence?"
For me, Brahman is not a God but the substrate that constitutes all things in the universe without any exception (living or non-living).