Paul is not asking his readers to reckon themselves dead indeed to sin, after they've verified that it is so, but before they've seen any evidence!
What happens if, right after the believer reckons himself dead to sin, he falls back into sin? Does this make the Word of God without effect (Romans 3:3)? Does this make God a liar? We can become disappointed and quit (which is what most people do), or we can repent and go right back to reckoning.
What happens then? God rewards our reckoning! He delights to see us believing in His Word when it seems impossible, believing God to be true though the evidence of his eyes contradicts God's Word (Romans 3:4)! And so He says, "Very well, you have believed having not seen; now you will begin to see the truth of what you have been reckoning!" And eventually we begin to see our reckoning producing fruit. Sin will be broken, not just in faith, but in sight. Victory will be ours, not just in principle, but in verifiable fact.
This is how we can contend against sin in a spirit of rest. Hallelujah!