Using can in this context, I am asking if it is possible that The Divine has a mind that is "changeable"? Or does Hashem's eternal nature preclude this?
The Torah states emphatically that Hashem does NOT change HIS mind in Shemuel I:15: 29
וְגַם נֵצַח יִשְׂרָאֵל, לֹא יְשַׁקֵּר וְלֹא יִנָּחֵם: כִּי לֹא אָדָם הוּא, לְהִנָּחֵם.On the other hand, in Breishit 6:6, it says "Vayinachem Hashem", that Hashem regretted His decision regarding the creation of Adam.
This is apparently a blatant contradiction.
R.S.R. Hirsch, in B'reishit makes an ingenious Diyyuq using Diqduq. In Shemuel, the reflexive Hispael is used, while in B'reishit, the Pi'el construct is used.
As such, in Shemuel the Torah is teaching that Hashem never changes his own mind - meaning in isolation or due to internal ruminations.
However, in B'reishit, Hashem is not altering his internal stance. Rather, He is merely reflecting the external change in Adam-humanity since Creation. Hashem's Mind is actually internally consistent; it is simply that external circumstances trigger altered responses.
This is different than humans who may indeed change their minds without external stimuli. Human minds can be fickle -
While G-d's mind cannot! However, His mind may appear to change - given a corresponding change in Circumstances - but never due to mood, etc.