The necessity of the Cross was to satisfy the Wrath of the Father.
The Cross was not a transaction between God and Man.
The Cross was a transaction between the Father and the Son.
There being no Atonement by fallen Men which could satisfy the Father's Wrath towards Sin, the Son agreed to provide the requisite Atonement. The Atonement thus provided, the Father unilaterally applies this Atonement to the accounts of His Elect, and unilaterally sends the Holy Spirit to regenerate those for whom Christ has atoned.
If grace is being dispensed at His good pleasure, then faith is really irrelevant.
Faith is no more irrelevant than breathing.
Breathing is what living people do.
Faith is what Regenerate people manifest.