If God is sovereign over all salvation like you say so, why pray/evangelize/do anything?There are a few responses:
The first is to say "well, the reason why we do these things is because God uses means in order to work the ends." Which is to say, "God is sovereign, so that's why we pray, that's why we evangelize, that's why we study the Bible, because we know God is at work as we do that, and all those things, are done in the Lord and by the grace of God."
Which is certainly a sufficient and able answer.
But the Bible never really just answers an objection and leaves it at that, but the Bible oftentimes goes after the objector as well. The underlying assumption to such a question is that "something needs to have practical results in order for us to do it." That assumption is ill-founded.
So another answer that works to undercut the question itself (though we do still have an answer to the question) is to question that very premise. Where in the Bible are we encouraged to only do things if they have a practical result? Or are we asked to obey because God asked us to obey?
The rewards that God promises us are not earned by our obedience, they are gracious gifts of God. On the last day, we will say that we were unworthy servants, for we have only done our duty. (Luke 17:10) It could be entirely possible that God will not use our prayers, will not use our evangelism, will not use our study of the Word. But we ought to obey simply because God asked us to pray, God asked us to evangelize, God asked us to study His Word. There is no other reason needed.
Don't get me wrong, God uses our obedience, and He uses it mightily. He promises rewards and treasures for those who give much for the kingdom of God. But those gifts are an act of grace from a loving God, not a "give-take" contract between two parties. So let's not motivate our actions by pragmatic results, but obey simply because God asks us to, trusting Him with all the results.