You do not have an EIN if you have not requested one through the IRS. An EIN is usually only necessary if you own a business and have employees.
On a tax return you will only need to enter your Social Security Number if you have taxable income to report on the tax return. However, if you do not have any type of taxable income to report on the return, there is no need to file a return, with or without a dependent since you cannot receive any type of tax credit for the dependent if you do not have taxable income.
Unless you also received a Form 1095-A for your health insurance through one of the State Marketplace Exchanges or from healthcare.gov then you must file a tax return.
The refundable child-related credits are not available to you if you did not have income from working. If your only income was Social Security disability, then you will not be eligible for the child tax credit or earned income credit. There was only one year in which that was possible---tax year 2021---and then the tax laws changed.
If TurboTax is asking you for an EIN, you are probably entering something in the wrong place. If that's what's happening, where in TurboTax is it asking for an EIN, and what are you trying to enter? If you're entering your disability income, is it Social Security disability? state disability? private disability insurance?
You cannot enter a W-2 if you did not actually receive a W-2 from an employer.
The money you hear about people getting for just filing a tax return claiming kids requires them to have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit. Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.