Is receiving the Qur’an in the mosque between the Maghrib and 'Isha prayers considered to be an attainment of the virtue of the first row, taking into account the Hadith: "If the prayer is established, he leaves his family as if he does not know them"?

The preponderant opinion is that the first row is the row directly behind the Imam. Engaging in learning and studying the Book of Allah is among the best acts of worship, and seeking knowledge takes precedence over other supererogatory acts of worship. Knowledge benefits both its seeker and the Muslims, it corrects acts of worship, scholars are the inheritors of the Prophets, knowledge is an attribute of Allah Almighty, and it is a communal obligation (fard kifaya). Therefore, your remaining with your shaykh to learn the Quran is better than being keen on praying in the first row. The hadith "And when the prayer is due, he would go out for the prayer" indicates promptness in performing the prayer when its time arrives, and you are already present in the mosque, so it is not suitable for drawing an inference in your situation.