When talking to an unbeliever about Christ, is it necessary to first prove that God exists?

In the first place, the Word of God presupposes that God exists and begins onthat premise (Gen 1:1). It therefore cannot be wrong for the child of God to dothe same.

Secondly, unbelievers may doubt the existence of God, but only a comparativefew will be downright philosophical atheists. In fact, experience teaches us,and the Bible affirms, that there are no natural atheists in this world. Man iscreated in the image of God and, despite the Fall, retains some knowledge ofthe existence of God. This is why man has a conscience which no irrationalcreatures have (cf. Rom 2:14). This is also why, no human society, no matterhow primitive or advanced, is without some form of religion (cf. Rom 1:20–21).In other words, atheists (i.e., philosophical, rather than practical, atheists)are made, not born. Attempts to prove the existence of God before proclaimingChrist may, therefore, turn out to be more distracting than beneficial.Nevertheless, we should take note that intellectual atheists are generallyunwilling to listen to the Gospel; and also that those with higher (godless andevolutionalistic) education, who are willing to listen to what we have to say,may sometimes need to be reminded that God exists and will judge us for oursins.

But thirdly, remember that the message of apologetics is insufficient forsalvation, while the message of the Gospel is absolutely necessary. Thus, it isoften prudent to disregard the possibility that our listeners may beatheistically inclined and go straight to presenting the Gospel. Faith andbelief in the existence of God are inextricably tied together (Heb 11:6). IfGod regenerates the sinner, his doubts concerning the existence of God vanishesinstantly.

Having said this, it must be admitted that there are occasionally situations inwhich highlighting the evidences for the existence of God, before speakingabout sin and the remedy in Christ, may be helpful. Such is the case if thelistener violently objects to the existence of God and therefore shuts his earto what you have to say. In my personal experience, a case in point would beintellectual scholars from China who have been systematically brain-washed bytheir communistic education system. In such cases, demonstrating the existenceof God may help the person to listen more attentively and with a less biasedattitude. However, the listener must be shown the unreasonableness of atheism,and also be informed that atheism is sin.