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There may be an alternate means of verification, but, in order to set up an account the SSA (Social Security Administration) needs to verify that you are who you say you are. They chose to use auxiliary information from your credit report, such as addresses and employers.
The FAQ at http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/2397 , states that you may be able to set up an online account at a Social Security office. A more specific FAQ at http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/2444/related/1 states that you can setup an online account only by removing the freeze on your Experian account or by visiting a Social Security office.