Ignore the Beginning Balance, for the First Reconciliation.
"I cannot enter the starting balance because all the transactions are already in the register"
That Source Document is not your point of reference for the Beginning balance, so Ignore it.
Your goal is always the Ending Balance. If you can reconcile all transactions that you know historically got processed and you get to the current Ending Balance with a difference of 0, you are fine.
Example: The Very First reconciliation always Starts at 0. That's because Beginning Balance is the Net of All previously Cleared transactions, and nothing has yet been cleared.