In Exodus 30:15 all men are to give one half shekel to "make an atonement for your souls."
Hebrews 9:22 says "And almost all things are by the law purged with blood; and without shedding of blood is no remission."
So is atonement in Exodus 30:15 something other than forgiveness of sin? Or is it an Old Testament precedent for Catholic indulgences, for payment for forgiveness?
Only by death is the guilt of sin removed. That can be the death of the sinner himself (Isaiah 22:14) if he burns in the lake of fire. Or it can be the death of our Creator, who became a man and carried our sins to His cross. His blood atones for sins. (Hebrews 1:3)
But in that last sentence, atonement is payment. That is how the word is used in Romans 5, the only NT use of "atonement" in the KJV.
That contrasts significantly with atonement in the Old Testament. There atonement is made for fungal infected homes, bleeding women, lepers, open wounds, for buildings, and in this passage, it is made by means of a cash payment.
It is evident that atonement in the Old Testament means "cleansing" rather than "payment for sin." The phrase "make an atonement for him and he will be clean," is typical of these usages. Leviticus 14:20
And this explains Exodus 30 where money spares men from plagues (v. 12). This is not remission for sins. It involves no repentance or change of heart. And this passage can't be used to justify indulgences or male-only salvation.
So briefly, in its one NT use, atonement is payment for sin, and so atonement was finished at the cross. It is used this way many times in the OT also.
But in the 70+ OT uses of this word, atonement is often cleansing and making things right, and even once it is making Noah's ark seaworthy. It is often similar to "cleansing" and in these usages it is not payment for guilt.
For a more robust and nuanced answer from me, see my article: https://bibledoc.org/the-day-of-cleansing-2/
Yes, Exodus 30:15 is clearly an example of atonement without the shedding of blood. (Although some Christian translators say "ransom" instead of "atonement" here, but the Hebrew word is the same.) There appears to be a misunderstanding here of what Hebrews 9:33 actually says. It says "almost all" not "all." Another example is found in Leviticus 16:
Taking the two male goats and setting them before the Lord at the entrance of the tent of meeting, 8 he shall cast lots to determine which one is for the Lord and which for Azazel. 9 The goat that is determined by lot for the Lord, Aaron shall present and offer up as a purification offering. 10 But the goat determined by lot for Azazel he shall place before the Lord alive, so that with it he may make atonement by sending it off to Azazel in the desert.
In the OP's example, atonement takes place by sacrificing money, not shedding blood. In the case of the scapegoat, atonement happens by setting the goat free in the desert, not shedding its blood. Another important example is Prov. 16:6:
By steadfast loyalty guilt is expiated (atoned), and by the fear of the Lord evil is avoided.
The OP asks if perhaps no sin was involved in Exodus 30. I don't think we can make this presumption. In addition, from a Christian viewpoint, John the Baptist offered baptism for the remission of sin, which is the same language used in Hebrews. In many cases someone had to be purified because they have become ceremonially impure (e.g. touching a dead body or engaging in marital intercourse). No sin is involved here but purification was still needed. This usually involved bathing. So there are actually many examples of purification without the shedding of blood. There are also sins which cannot be atoned for by blood sacrifices. This include adultery, murder, blasphemy, idolatry and others.
