You ask, “If God is sovereign, why does the Christian need to share the Gospel?”

For starters, we are commanded and commissioned to, by no less than Christ Jesus.

“Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit and teaching them to obey everything that I have commanded you. And remember, I am with you always, to the end of the age.” - Matthew 28:19-20

And by what means are we to evangelize and disciple others?

“So then faith cometh by hearing, and hearing by the word of God.” - Romans 10:17

“All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works.” - 2 Timothy 3:16-17

“How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher?” -Romans 10:14