Yes, we can be sure God has forgiven us -- once we understand what Jesus Christ has done for us, and trust Him alone for our forgiveness.
Let me illustrate it this way. Suppose you were carrying a very heavy burden -- so heavy that you knew it would crush you if you kept carrying it. But then suppose someone came along who was much stronger than you, and offered to take the burden and carry it for you. What would you do? The logical thing would be to hand it over to him -- and once you did, you'd be completely free of it the rest of your life.
This is what Jesus Christ did for us. Our sins are like that burden -- a burden so great it will destroy us eventually. But on the cross Jesus Christ paid the penalty for all our sins -- and now He offers to take that burden of sin from us. All we have to do is turn it over to Him -- and it's gone forever! Jesus' promise is for you: "Come to me, all you who are weary and burdened, and I will give you rest" (Matthew 11:28).
By a simple prayer of faith commit your life to Jesus Christ, repenting of your sins and trusting Him alone as your Lord and Savior. Then thank God that even when we do sin, "we have one who speaks to the Father in our defense -- Jesus Christ, the Righteous One" (1 John 2:1).