Excellent question here, and one that is quite instructive more generally.
Throughout this chapter, Paul makes a clear distinction between God the Father and the Jesus. Let us observe the following:
- V1: Christ Jesus by the will of God (Θεοῦ)
- V2: To the church of God (τοῦ Θεοῦ) in Corinth, to those sanctified in Christ Jesus
- V3: Grace and peace to you from God (Θεοῦ) our Father and the Lord Jesus Christ.
- V4: I always thank my God (τῷ Θεῷ) for you because of the grace of God (τῷ Θεῷ) given you in Christ Jesus.
- V9: God (ὁ Θεὸς), who has called you into fellowship with His Son Jesus Christ our Lord, is faithful.
- V24: but to those who are called, both Jews and Greeks, Christ the power of God (Θεοῦ) and the wisdom of God (Θεοῦ).
In V25 we have: For the foolishness of God (τοῦ Θεοῦ) is wiser than man’s wisdom, and the weakness of God (τοῦ Θεοῦ) is stronger than man’s strength.
Note that "God" throughout this passage occurs in both the articular (ὁ Θεὸς) and inarticular (Θεὸς) forms. Generally (with a few important exceptions that the grammar and context makes clear) the articular ὁ Θεὸς refers to God the Father.
However, in this chapter of 1 Cor 1, the distinction Paul consistently makes between God (the Father) and Jesus is quite evident and obvious. Therefore, "God" consistently refers to the Father, including V25. We see that same distinction made again in V30.