Would the girl be considered my wife Islamically after we pledged to marry each other by the Qur’an, and kissing and foreplay occurred between us without intercourse, and we called upon Allah and His Messenger to witness that?

The girl is not your wife, and you are not her husband. Each of you is a stranger to the other. Caressing and kissing between you are forbidden by Islamic law, and you must repent from them. Legitimate marriage has rules and conditions, none of which have been met between you. The pledge that occurred between you holds no value in Islamic law. You must fear Allah. If you desire her as a wife, then propose to her family and complete a valid, legitimate marriage with a guardian and witnesses.