Isn't that what led to the problem in the first place ?
No, it acts as a sieve. Free Will is not a ‘cause’, it is a mechanism to sort God’s Will from human will; sorting Life and Death.
Lucifer and Adam chose wrongly but certain Angels chose rightly.
But God loved Adam and sent his Son to be in effect to be the perfect Adam that chose rightly to follow God’s Will; “be it Your Will, not Mine”.
We suffer because of Adam, not because of God. But we know our suffering will be removed by He who died for us and conquered death by His Resurrection.