Yes, Gautama Buddha had 32 major qualities, as do all Buddhas a.k.a. one who has attained the dharmakaya, sambhogakaya, as well as the nirmanakaya--the latter two of which correspond to the physical attainments.
These physical attainments progress according to the Taoist timeline of physical transformation of jing, chi, shen transformation but in Buddhism, which focuses on Wisdom, it is not necessary to focus on the physical aspect because this occurs automatically when one's mind is in the right place (Four Noble Truths, Right Samadhi, 8 + 2 Eightfold Path).
His mind is a mind free from the skandhas.
As for atman... He experientially discovered that there is no atman, that it is a causation illusion via the aggregates/skandhas, that we are the an ocean of interdependence... of Self and thus paradoxically, he attained the true Atman, the dharmakaya, becoming free from birth-and-death and forever serving ourself as a Buddha because such a perfectly compassionate immortal has nothing better to do with their time... this didn't happen at once and occured in a step-wise progression through the Four Noble Truths (which includes letting go of the things that bind one to Atman).
The above idea would be a Mahayana and Tibetan idea... less a Theravadin idea which insists on "annihilation" of self... (which in a sense is the same meaning because one annihilates oneself into the Buddhahood of serving others manifesting limitless skillful means and having uprooted one's poisons and afflictions already...)