Order matters. Sometimes it matters more than others.
If you pour espresso shots in followed by steamed milk it’s a latte, if you pour the shots in after the milk it’s called marking it, so a macchiato (while also sometimes true that a macchiato has less steamed milk). In general it’s the same ingredients, and the different order makes for a different name.
Certain mathematical operations require a particular order. It’s not just what’s it’s called, but the answer is different. In a string of numbers and operations, multiply within the parenthesis then add (follow the acronym PEMDAS for more). It’s not two ways of getting to the same answer, it’s wrong.
The peace offering in the Old Testament did not come first, nor was it typically held on its own. The peace offering came after some other offering, regularly the sin offering as well as the burnt offering. Sins were atoned for, the worshipper was consecrated to the Lord, then food was shared.
If we tried to start at the Lord’s Table in our Lord’s Day liturgy, we’d certainly have to come to the Supper differently. But because we have it when we do, after confession of sin and consecration by the Word, we are ready to celebrate. We are not damned. Christ damned our sin to death. Christ’s death ruined sin’s tyranny. “We have peace with God through our Lord Jesus Christ” (Romans 5:1). There is no condemnation for those who are in Christ Jesus” (Romans 8:1).
The correct order is Christ’s work and then our worship. The correct order is faith and rejoicing then obedience. We do not work ourselves into the Supper, the Supper works its way into us by grace.