Box 13 on the 1099-R is not the annuity start date. The annuity start date is the first day that you received a distribution from the annuity.
If you don't have this date anywhere on your paperwork (has it been so long that you don't remember when you first get a distribution from the annuity?), then contact the annuity administrator (the Payer in the upper left corner of the 1099-R) and ask them.
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