No that would be salvation by works. Jesus not only dealt with those sins under the old covenant, but he also paid for and redeemed ALL sins :
The Messiah died for all sin.
His
death was once, for all. He doesn't need to die again. It is finished.
...but the work of "mediation" and "cleansing of a guilty conscience" with His
blood is a separate work that happens
in time, one person at a time. This is why we needed an
immortal High Priest. Can't cleanse the guilty consciences of believers not yet born, you know? The believer's conscience doesn't exist to cleanse until the believer exists. And cleansing doesn't begin until the believer confesses. So we needed a pure priest who lives for a LONGGG time.
If all cleansing of all believers (for all time) happened at the moment of His death we wouldn't currently need a High Priest with an
indestructible life, but Hebrews specifically points out this unique quality that makes all the difference.
Hebrews 7:16 [brackets mine]
who has been constituted [as priest] not according to a law of a fleshly commandment, but according to the power of an indestructible life.
The power of salvation isn't found in faith in Messiah's death, but in faith in His
sinless blood that cleanses. Faith in His life. Our faith is supposed to be in what He's doing for us
now in heaven and in our hearts.
Comparatively, works-based salvation would be me believing I can somehow
cleanse myself of my sin guilty by doing good works or obeying the law. Again, I need the Messiah for that.
13And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
14Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
Maybe this example will help:
Let's say you bought a house that hasn't been lived in for years and years. And no one has kept it maintained in all that time so the dirt and filth has mounted room to room.
You buy the house and spend a week cleaning every room...and at the end of the week you look at the house and conclude that "
all filth has been cleaned from my new home", which is true, so you furnish the house and move in.
But question: Was this the only time you'll ever clean your new home...or will you work to keep your home maintained, cleaning it weekly, monthly, and/or seasonally? What if a spill occurs or someone makes a mess in a specific room? Will you leave the mess or will you clean it up?
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It's TRUE that when we were dead in our sins through faith in the Messiah we were forgiven of
all of them
that we committed...but unless we somehow instantly became perfect we were bound to stumble and sin again in the future, which is why we are told to go boldly to the throne in our time of need and confess the sin to keep ourselves clean. The Messiah does the rest.
Then when we're clean again we do our best not to sin, to obey, and to do good.