From what I gathered, EIN may not be required but most small business advisors, and as you say the Michigan Treasury website, recommend that you apply for an EIN, (also called FEIN if it is a Federal Tax Id Number ) and use that number instead of the Social Security Number.
A Federal Tax Id Number is required for employers and corporations as well as partnerships, though sole proprietors may also get it.
If you google online there are a lot of services offering to get this number for you, do not fill out their forms, because there are also a lot of unsafe phishing sites. It will be smart to go directly to the IRS -
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In the IRS website, getting EIN online doesn't seem to be a daunting task.
It says "No need to file a Form SS-4. We ask you the questions and you give us the answers. After all validations are done you will get your EIN immediately upon completion. You can then download, save, and print your EIN confirmation notice."
Hope I got them right. :)