We are told to realize something that is already true of our position or status. It is not an exhortation to us to do anything with regard to sin, but to realize what has already been done for us with respect to our relationship to sin. It is an exhortation to us to remember what is already true of us... And what is true of us is that we are already in an entirely new position and standing with respect to sin.
This is something which we have to believe solely because the Word of God teaches it. You do not 'experience' your position, you are told about it and you believe it. That is what justification by faith alone means.
...We have all got to do what Abraham did. We must just take the bare Word of God, believe it, submit to it, and act upon it. That is what we have to do with this statement.
(Romans 6: The New Man, (Carlisle, PA: Banner of Truth Trust, 2008), 120.