It is a valid observation that, in the book of Acts, proclamation of the gospel message often came as an explanation of some work of God in people’s lives. It is equally valid to say that we should, therefore, be looking for such works of God and taking the opportunity to offer a similar explanation. What is omitted from the quotation above is the fact that the works of God themselves involved the active participation of the apostles.
In the Acts 3:12 example, God healed the beggar in the name of Jesus by the power of the Holy Spirit, but he did it in response to action on the part of Peter and John. They saw a need, were moved by compassion to act and did so, drawing on the promised power of the Holy Spirit. Being alert to what God is doing in our situations is important, but I venture to suggest that what He will be doing is likely to involve us first recognising need, being moved to act and doing so, drawing on that same promised Holy Spirit power.
We may not see miracles of healing or whatever, but we may well see openings for a gospel explanation, followed by the miracle of changed lives. Among the Christian Unions in UCCF we simply call this living and speaking for Jesus.