Some sole proprietors do not use an EIN and run their business under their SSN. However, to establish a Solo 401(k), you will need an EIN for your business. The EIN must be listed on the adoption agreement.
It is important to keep your retirement plan dollars separated from your personal dollars.
Once your plan reaches $250,000 in assets, you will be required to file Form 5500 with the IRS, which asks for the plan sponsor's EIN. Prepping for this ahead of time will avoid a potential audit.