When consideration of terms such as immutable, one is confronted with a certain level of dilemma.
There are those who would perceive God as flexible and adapting.
There are those who would view God as rigid, inflexible.
The word immutable, does certainly carry as synonyms such as rigid, inflexible, unchageable, set, fixed ..., however immutable is not completely synonymous (imo) with the limit of these types of characterizations.
Rather, immutable has the background of not being able to be mutated. Biologically or chemically altered.
As it relates to God and focusing upon His character, it is that His character is consistent, His purpose unthwarted, His holiness unspoiled...
As it relates to humankind, immutable means that God's vows do not change, His statements have full veracity, that complete trust and reliance are securely held because He doesn't even have the flitting thought of modification or mutating into that which would violate Himself.
Unlike humankind, who can be "double minded" confused, perplexed, ... God cannot.
However, does God actually change in how He presents Himself to His creation?
To some, they would suggest He does "appear" to change as more is revealed in Scriptures about His character and purpose. Adam may have not seen these as changes at all, for no other has walked and talked as Adam and God. But human perspective is always marred by the influences and pressures of the human condition.
So, is God immutable?
Perhaps. Did not Christ change from the glory He had with the Father to take upon Himself the form of man? Was this not a forever condition that literally changed God?
Did God actually go through a biological mutation?