1 Thess 1:4 For we know, brothers and sisters loved by God, that he has chosen you, 5 because our gospel came to you not simply with words but also with power, with the Holy Spirit and deep conviction.
The apostles are affirming the Thessalonians as the elect because God worked mightily through the apostles.
What I believe the underlined words might refer to:
"power" => God's
manifestation through healings and miracles (Luke 8:46)
"the Holy Spirit" => God's
presence, while the apostles preached, and in laying on hands for them to receive the Spirit
"deep conviction" => many of them turned away from idols and wholeheartedly were
convicted of their sins, the text continues how they became example to many believers in faith and totally turning away from serving idols
Half of translations have "assurance". Either way I think this refers to their conviction, strong faith in their heart that God is true.
https://biblehub.com/greek/4136.htm
https://biblehub.com/greek/4135.htm