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You will forever be required to PG on sole proprietorship (SP), which is merely a DBA for you personally.
SP has no protection from liability or creditors. Your creditors or other liabilities can pursue you personally for all obligations of the business.
So, it depends on your strategy and desires.
But to answer your original question, yes, once you have an EIN, you can apply for business credit, more accurately described as personal credit for business use in your case.
In fact you don't even have to have the EIN if you are SP.
The only time you need an EIN when your a sole proprietor is when you have employees for payroll taxes. If you don't have employees you would use your SSN.
You may want to look at becoming a single member LLC. You may use an EIN or your SSN for tax reporting.You can elect to be taxed as a corporation or a sole proprietor. Becoming a SMLLC would afford you the protection you wouldn't have as a sole proprietor unless your going to carry adequate business liability insurance for your SP.
Try to find a good CPA, they are worth their weight in gold!