God is sovereign over salvation. He uses means, such as gospel preaching but also works directly opening the hearts of His own so they hear and believe.
Salvation belongs to the Lord; your blessing be on your people! Psalm 3:8
One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul. And after she was baptized, and her household as well, she urged us, saying, “If you have judged me to be faithful to the Lord, come to my house and stay.” And she prevailed upon us. Acts 16:14-15
The Psalmist was in dire straits. According to the title of Psalm 3, David wrote this during his exile from Jerusalem while his son, Absalom, briefly overthrew his father’s kingdom. David turned to God in the crisis, recognizing that only the Lord could save him. “Salvation belongs to the LORD,” he affirms. Absalom had skillfully won over the people of Israel to support him. David fled Jerusalem. But it seemed inevitable that David would be assassinated and Absalom would take firm control of the kingdom.
Yet, “salvation belongs to the LORD.” David held to that truth, and, against all odds, Absalom listened to David’s planted advisor, Hushai who purposely gave him bad advice. Absalom followed it, and died in the ensuing battle (2 Samuel 17-18). God saved David’s life and kingdom. The odds set by probability cannot limit God.
Lydia was a worshiper of God, a Gentile woman who believed in the God of Israel and the moral law of Moses without adopting the dietary and ceremonial laws. Luke tells us that the Lord opened her heart to pay attention to what Paul said. Without the intervention of the Holy Spirit, neither a Lydia nor anyone else is able to hear and believe the gospel (Jeremiah 13:23; John 6:44, 65; Romans 9:16; 1 Corinthians 2:14; 2 Thessalonians 2:13-14; 2 Timothy 1:9-10). God saved Lydia spiritually. 
Think about it
God saves kings and Gentile women, like David and Lydia. How does the truth that “salvation belongs to the Lord” affect your prayer life and your daily confidence in Him? Can you lie down and sleep, knowing the Lord will sustain you? Trust Him when in danger for He saves. Proclaim the gospel to others knowing that God opens hearts as He wills and saves lost people.
 The Reformation Study Bible notes p. 1945