The word “by” is a preposition, used to identify the agent, which in this case would be the Cross with which an action was performed, which indicates the means of achieving something, and in this instance it is Christ’s death for our sin.
By = action, achievement.
“And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:” ~ Ephesians 2:16
If Paul used the word “at” instead, it would have a different meaning entirely, expressing the location or time where the action or achievement took place, that is at Calvary, almost 2000 years ago.
It is Christ’s achievement on the cross which matters and is important because it is what saves one’s soul, not the time and location of the deed, this is why Paul uses the term “by the cross”, and not “at the cross”.
“For the preaching of the cross is to them that perish foolishness; but unto us which are saved it is the power of God.” ~ 1 Corinthians 1:18