Fresh grad with nothing other than a piece of paper awarded by teachers who have hardly spent enough time in the corporate world?
With triple E, I guess you are very strong in it? So...
What are you braggable achievements, Like... how many patents do you have?
What was the biggest deal you secured for any company? 10 million USD?
What designs have you participated in that was released into market which generated how much revenue?
What is the biggest problem you solved for any corporate world company? Like helping some mobile phone companies like Samsung sort out some quality problems? How much was the statistical reduction in nonconformities?
What was your yield when you implemented any changes that supposedly helped in design?

If you cannot answer any of those questions, and STE is honestly not a good place to learn. Go and look for large corporate companies that are open to fresh grads, pick that role up and spend 12 months on that role. Build up your profile and learn something. Life will be hard but at least rewarding because you learn something. There, you will learn their supply chain network, know their customers and suppliers and move along that line.

And whatever fairy tales you heard in school, validate it with the real world.

No short cut.