Requiring a clearance at start is not an unusual requirement, especially since they want someone who already has 12 years of experience. Except for new graduate jobs, I'd say that 95 percent of the DoD jobs in the DC area require a clearance at start. Also note that they are giving you a break on the TS/SCI clearance - they are willing to pay for that and wait for it to be adjudicated. That is noteworthy.
Since it's a contractor job, you can always apply and explain your situation. For a highly qualified person, they might be willing to bend a little. Sometimes an interim secret can be granted almost immediately. Finally, it may not be the contractor's fault. The terms of their contract may stipulate that the person hired have a clearance at start. The government may not want to pay for someone while they wait for their clearance, and the contractor doesn't want to put the person on overhead while they are waiting for a clearance.