Gospel optimism is about the gospel being deep and wide. We should expect the gospel to penetrate and conquer with geographical breadth (to the ends of the earth) but also with personal and social depth. After all, the gospel says (among other things) that Jesus is Lord, the judge and saviour, the rightful king of our world, the one in whom humanity and in fact all of creation is reconciled and transformed.
A while ago I posted on this. Then yesterday I found a quote by Abraham Kuyper.
It is not that there are two worlds, a bad one and a good one, which are fitted into each other... it is one and the same world which once exhibited all the glory of Paradise, which was afterwards smitten with the curse, and which, since the Fall, is upheld by common grace; which has now been redeemed and saved by Christ, in its center, and which shall pass through the horror of the judgment into the state of glory.
Kuyper goes on to explain the 'cash value' for Christian living of viewing the new creation as a renewal of the present earth rather than an entirely new thing.
For this very reason the Calvinist cannot shut himself up in his church and abandon the world to its fate. He feels, rather, his high calling to push the development of this world to an even higher stage, and to do this in constant accordance with God’s ordinance, for the sake of God, upholding, in the midst of so much painful corruption, everything that is honourable, lovely, and of good report among men.
Thus gospel optimism means that none of our labours done in Christ's name (not just our evangelism) are in vain because of Jesus Christ.