Inside the ark lay the broken law. On top of it, a golden lid where blood was sprinkled and God promised to meet. Paul uses that lid's own name for Jesus.
The Shadow
The ark of the covenant held the tablets of the law — the covenant Israel had already broken before Moses got down the mountain. If the ark had been left open, the law would have faced the people bare, and the law bare is a verdict. So God commanded a lid: pure gold, cherubim bending over it, called the mercy seat. Once a year the high priest sprinkled blood on that lid, so that when God looked down He saw not the broken law but the blood that answered it.
And God attached His presence to that exact spot: And there I will meet with you, and I will speak with you from above the mercy seat. Not above the tablets. Above the blood that covered them. The meeting place of God and sinners was, by God's own design, the place where the law's demand had already been answered.
The Fulfillment
When Paul explains the cross in Romans 3, he says God set forth Jesus as a propitiation by His blood. The Greek word Paul chose is the word the Old Testament's Greek translation uses for the mercy seat itself. Paul is not saying Jesus made a payment somewhere in the bookkeeping of heaven. He is saying Jesus is the meeting place — the true golden lid where the law's demands and God's mercy meet, publicly, at the cross. John says it without the furniture: He Himself is the propitiation for our sins. Not He arranged it. He is it.
Him All Along
When God deals with you, He does not deal with you over the bare law. He meets you at the mercy seat, and the mercy seat is His Son. Every accusation the tablets could make has blood standing over it — blood that speaks better things, and never wears out. The place where God meets you is not a courtroom. It never was. It is a mercy seat, and it is occupied.