Before the elect believed, Christ had already purged their sins Heb 1:3
3 Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high:
Not only before we believed, but before we sinned, our sins had been purged, that we would commit. In fact He had purged them before He went back to the Father and sat down on His Right Hand of Majesty.
This had been accomplished by Himself, that is by He offering Himself as a sacrifice for our sins. In another place its said He took them away Heb 10:11-12
And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins:
12 But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God;
So legally before the Holy Justice of God the elect are saved from the penalty of their sins before they believe, because their sins have been purged away.
Ps 79:9
Help us, O God of our salvation, for the glory of thy name: and deliver us, and purge away our sins, for thy name's sake.
When Christ by Himself purged our sins, It made Him the God of our Salvation, and it was to the Glory of His Name !