Some think that finance is some special place where mortals cannot tread. I have found that people who are completely unfamiliar are often the breakthrough people. They do not carry preconceived ideas that limit their ability to help. They may ask very basic questions that reveal otherwise unthought of ways to improve. I am not saying that private companies have to give up all confidentiality in their finances.
For example: I worked with a company where an urgent payment took a week to process to start getting the needed part for a machine. No one dared say anything as the finance department reported overseas. So the next similar event took even longer.
And be certain that coworker engineers checking things out brings a lot more change than the boss bringing pressure. Create mutuality. It really gets the business going. It is also a form of cross training and development.
And get the finance people checking out engineering as well. We all need another set of eyes. The more we encourage people to check on and respectfully enter another area, the better.