Is the row parallel to the Imam considered the first row, even if it occurs daily, in cases where the prayer area is not sufficient for all worshippers?

The first row is the one directly behind the Imam. The reward of the first row is not attained by those who stand to his right or left, because the Sunnah is for the worshiper to stand behind the Imam. Standing to the right or left is permissible when needed, and it is better than waiting for the first row to become empty.