If you are filing estimated tax payments for your personal return, including a Schedule C business (single member LLC or sole proprietorship), then you can still use the regular IRS payment processing site for an estimated tax payment at the link below. The estimated tax payment will be credited to your SSN.
The EFTPS is very convenient and well regarded, but it is not required unless you are a business return - i.e. C Corp, S Corp, multi-member LLC, etc. So, you can make this initial payment using the regular payment system (select Estimated Tax Payment from the menu options for type of payment) and then scheduled the rest of the payments for the year with the EFTPS.
https://www.irs.gov/payments