There is not a workaround. In order to get this credit, your son would have to attend an eligible educational institution. If your son did not attend an eligible institution that is listed with the US Dept. of Education, you would not qualify for the American Opportunity Tax Credit. This is the reason it is requiring the EIN.
"An eligible educational institution is a school offering higher education beyond high school. It is any college, university, trade school, or other post secondary educational institution eligible to participate in a student aid program run by the U.S. Department of Education."
https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/eligible-educational-ins...
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