Romans 3:22a says, “This righteousness from God comes through faith in Jesus Christ to all who believe.” God’s saving righteousness (declaring a sinner to be in the “right”) comes “through faith in Jesus Christ.” The phrase “faith in Jesus” is synonymous with trusting in Jesus, believing in Jesus, anchoring our hope in Him alone. We are saves by sola fide (faith alone), not faith+works. The basis of our being made right with God is faith alone.
The “through faith” expression is used elsewhere in a context of salvation. For example, Paul says, “For it is by grace you have been saved, through faith…not by works, so that no one can boast” (Eph 2:8-9). That final phrase of Ephesians 2:9 (“so that no one can boast”) is the reason why “through faith” must be the sole basis, and not “faith+law-keeping.” If I kept the law, and that law-keeping added to the basis on which I was “right” with God, I could have room to boast! God will simply have none of that, no grounds for human boasting. So God saves by His grace “through faith” and “not by works.” In this way, God receives all the glory for salvation. As it should be.