His salvation occurred while the Old Covenant was still technically in effect, as our Lord had not yet died. But I am uncomfortable with treating salvation as being fundamentally different for those before our Lord than those after our Lord. Abraham, after all, was not saved under the Old Covenant, but the New; for we are told that Abraham had faith and it was accounted to him as righteousness; our Lord Himself says that Abraham looked forward to Christ's day. The same is true of Moses and indeed all the Patriarchs and Prophets.
The Old Covenant has no provisions for salvation, it wasn't given for that purpose. Thus none was ever saved "under" the Old Covenant; rather they were saved under the New. Even before the New was enacted by the death and resurrection of our Lord, it is by His shed blood and atoning work that any one is saved. Whether in the Old Testament or the New. Whether we talk of the Patriarchs or of ourselves today.
To that end, I'd argue that the thief was saved without Baptism because A) Jesus had not yet instituted Holy Baptism and B) The power of salvation is God's to wield absolutely as He so sees fit, and thus when Christ says, "I speak honestly to you, today you will be with Me in Paradise" we can trust in the word of Christ here.
That same word, "You will be with Me" is the word we receive in Holy Baptism. Through Baptism we are born again, receive the full remission of our sins, are united to Christ, to His death, burial, and resurrection. And thus to whomever the Lord says, "You will be with Me" to whomever the Lord says, "Your sins are forgiven", to whomever the Lord declares His own, are indeed His, are forgiven, and indeed have eternal life. Baptism is this same word of Christ, in visible form,
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Husbands, love your wives, as Christ loved the Church and gave Himself up for her, that He might sanctify her, having cleansed her by the washing of water with the word, so that He might present the Church to Himself in splendor, without spot or wrinkle or any such thing, that she might be holy and without blemish." - Ephesians 5:25-27
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'Now you are clean through the word which I have spoken unto you.' Why does He not say, 'You are clean through the baptism wherewith you have been washed', but 'through the word which I have spoken unto you,' save only that in the water also it is the word that cleanses? Take away the word, and the water is neither more nor less than water. The word is added to the element, and there results the Sacrament, as if itself also a kind of visible word." - St. Augustine of Hippo, Tractates on John,
Tractate 80.3
-CryptoLutheran