The evidence is simple: the incarnation, life, death, resurrection and ascension of Jesus Christ.
This implies that God the Father could not do what Jesus Christ has done - therefore He either was not, or is not, omnipotent (by any simple or sensible understanding of omnipotent).
With suitable qualifications, this is a powerful and basic truth; and may serve to help shake free from the deadly and paradoxical tyranny of over-focusing on God's abstract, absolute omnipotence.
Note: If this statement sounds fanciful - try to imagine how Christianity looks to a Non-Trinitarian strict-monotheist - who would surely find it incomprehensible that a genuinely omnipotent God (who supposedly created everything from nothing and makes absolutely everything happen absolutely according to His will); apparently cannot achieve what He wants to achieve for Man without the rigmarole of incarnating Jesus Christ as a Man at a particular point in history!
My impression is that the underlying situation is that real Christians don't really believe that God is omnipotent - but don't like to state that He is not ; are indeed scared to state that He is not omnipotent - since this sounds disrespectful, asking-for-trouble, and is certainly liable to lead to vehement accusations of blasphemy.
But I regard this as evidence in favour of the truth of the statement that God is not omnipotent - since to be deterred by fear, when God is our loving Father, suggests that omnipotence is in fact a demonically-inspired error; because to submit to a God conceptualized as being of un-limited power, from terror of the consequences of denying His power - is profoundly anti-Christian. It is indeed to subvert and invert God.
That is why this error of omnipotence needs to be tackled head-on.