I think that the "average American" experienced one, maybe two, attitudes towards big business philosophies during the ages of Industrialization. One one hand, there was a certain embrace of these justifying philosophies. Consciously or not, average Americans bought into the idea of wealth as being something that can be acquired through hard work and due diligence. The implication here is the embrace of the opportunity ideology that many of these philosophies such as free market justifications and social Darwinism was that average Americans accepted. It allowed them to feed their own dreams of success in that they believed that they, too, would and could experience their own portion of the American economic pie of success that drove the wealth of the "titans of industry" at the time. Another attitude that was experienced was the Progressive movement, which advocated that the "other half" of the economic success equation needed to be substantiated. Progressivism was an attitude or set of philosophical premises that many average Americans were able to embrace because it spoke to their own predicament and experience. For the many Americans whose narratives were not supported by those stories of the Carnegies and Stanfords, there were those of workers' rights, fair compensation, and the idea that American political and business orders needed to speak clearly for the experience of workers and those who might have been marginalized by said orders. In this light, Progressivism became an attitude or philosophy that average Americans were able to accept in governing their own feelings towards big business during Industrialization.
By industrial supremacy I am assuming you mean the Gilded Age in the late 19th century, when business and government were closely allied, and workers had few right and protections.
The attitude of the "average" American (and it is hard to say during this time of heavy immigration and migration what an average American would look/think like) during this time was a little complicated. Then as now, Americans worked hard each day and valued work. They were individualists who believed people should take care of their own families and be responsible for them. Entitlements did not yet exist and unions were, for the most part, illegal.
There was also virtually no middle class in America at that time, and the average American lived in poverty, with the gap between them and the wealthy as large as it has ever been in our history. They believed big business philosophies like laissez-faire capitalism (no government regulations or restrictions on business) were exploitative of the working class, and that wages were too low and worker safety non-existent. They supported Carnegie's Gospel of Wealth in terms of its philanthropy, while questioning the manner in which he amassed his fortune, along with that of J.P. Morgan and John D. Rockefeller. They challenged Social Darwinism's claim that the rich deserved their wealth, and that the economy needed to be purely survival of the fittest.