God does have a plan for our lives. It is plainly stated in scripture. But if you mean does God have one person set aside for you, there is no biblical evidence of this. Adam and Eve are not evidence, though some people try to twist it to mean that.
Reality is the idea of one person being made for another stems from pagan mythology, not bible teaching. Paul, who wrote much of the NT, obviously did not share this view either. He says only to marry if you burn with lust, otherwise don't marry so that you can live a life dedicated to God. How can we only choose to marry if we need to to help control our lusts if God has a person set apart for us?
Though the bible doesn't make any clear mention of this topic outside of Paul's opinion, the most obvious conclusion would be that there is no single person meant for us, but rather that there are numerous options for us that would be more ideal than others. And we would seek God to find one of these people.