Zach Wilson, the quarterback for the New York Jets, began his NFL career in the 2021 season. To determine how many wins he has against teams that finished the season with 10 or more wins, we need to review his performance in each season he has played.

- **2021 Season**: The Jets struggled overall, and Wilson faced several strong teams. Notable games include losses to the New England Patriots (twice), Buffalo Bills (twice), and Tampa Bay Buccaneers. Wins against teams that finished with 10 or more wins were rare.

- **2022 Season**: Similar to the 2021 season, the Jets faced several tough opponents. The specifics would need to be updated based on the final records of the teams he faced.

As of now, Zach Wilson's wins against teams that finished with 10 or more wins are limited. For an exact count, you would need to cross-reference each season's schedule with the final standings for those years.