Why didn't God send a miracle to the people of 'Ad like He did to other nations, and why didn't God punish the people of Ibrahim despite their attempt to burn him?

Every prophet was supported by miracles and decisive proofs indicating his prophethood, as Allah Almighty said: {Indeed, We sent Our messengers with clear proofs}. And the Prophet, peace and blessings be upon him, said: "There was no prophet except that he was given signs the like of which people would believe in; and what I was given was a revelation that Allah revealed to me."

As for the great miracle of Hud, peace be upon him, it was the strength of his trust and reliance upon Allah, as he challenged them despite their tyranny, saying, as Allah Almighty states: {Indeed, I have relied upon Allah, my Lord and your Lord. There is no creature but that He holds its forelock. Indeed, my Lord is on a straight path.}

As for Allah not punishing the people of Ibrahim in this world, that is due to a profound wisdom known to Allah. He punishes whom He wills and gives respite to whom He wills. It is not necessary that every disobedient person be punished in this world; otherwise, {He would not have left upon it any creature}.