Do we need to build a relationship with someone to Evangelize them? No. No where did Jesus say "Go and make relationships and then preach the gospel". Rather He said in Matthew 28:19-20 "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,
teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age."
Where did this teaching of friendship evangelism come from. Should we preach the gospel to those we know? Of course but also those we don't know. Irregardless of the culture or the situation. Paul said in 1 Corinthians 9:22 "To the weak I became weak, that I might win the weak. I have become all things to all people, that by all means I might save some." And he explains more in verse 23 "I do it all for the sake of the gospel, that I may share with them in its blessings." He doesn't say he becomes their friend and slowly over time try's to share the gospel because as it says in Proverbs 27:1"Do not boast about tomorrow, for you do not know what a day may bring. ".
We are not guaranteed another day, or another minute for that matter. The point is, is that we should be doing what it says in 2 Timothy 4:2"preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching.". We should care about the lost and pray for them. Most of all, we should share the gospel with them in love and kindness but not altering it in anyway. It's our job to preach and the Holy Spirits job to change hearts. John 16:8-9 says "8 And when he comes, he will convict the world concerning sin and righteousness and judgment: 9 concerning sin, because they do not believe in me;".
Lets remember what our role is and what His is. "Nothing to the cross I bring, ONLY to the CROSS I ClING".