Is it permissible to look into the eyes of a woman conducting a job interview, knowing that not doing so might give a negative impression?

Your excuse for looking at foreign women, under the pretext of seeking lawful provision, is not permissible. Provision is in the hand of Allah, and it is not attained through disobedience to Him. Allah has promised the pious that He will provide a way out for them and sustain them from where they do not expect, as He states: (And whoever fears Allah – He will make for him a way out. And will provide for him from where he does not expect) [Quran 65:2-3]. As for what your teachers say, it contradicts the words of Allah Almighty: (Tell the believing men to reduce [some] of their vision) [Quran 24:30], and the saying of the Prophet, peace and blessings be upon him: "Avert your gaze." Therefore, I advise you to adhere to piety and distance yourself from the forbidden so that Allah may ease your affairs.