Was it Gods purpose that Adam sin/transgress ?
Yes indeed, the sin of Adam was Purposed by God for a redemptive purpose in Christ.
Eph. 1:9-10
9 Having made known unto us the mystery of his will,
according to his good pleasure which he hath purposed in himself:
10 That in the dispensation of the fulness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him:
Eph. 3:9-11
9 And to make all men see what is the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:
10 To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God,
11
According to the eternal purpose which he purposed in Christ Jesus our Lord:
