Both things can happen. The government can pay for the bridge in the immediate term, and the company can be sued to reimburse the government. It's a subrogation concept. I dealt with it all the time when doing God's Work.
Suppose you're a Medicare recipient and get in a trucking accident. You get rushed to the hospital with injuries. The trucking company is ultimately responsible for your medical bills, but that process can take months or even years to sort out. Accordingly, Medicare is going to pay the bills up front. However, if and when you go after the trucking company, Medicare will have a lien against your recovery for what they paid out, and both the trucking company's insurer and your lawyer (if you have one) are legally required to reimburse Medicare before paying you anything. Same thing can happen with this bridge. The government can rebuild it now, and when the shipping company's liability is sorted out and adjudicated, the government can be reimbursed.
Suppose you're a Medicare recipient and get in a trucking accident. You get rushed to the hospital with injuries. The trucking company is ultimately responsible for your medical bills, but that process can take months or even years to sort out. Accordingly, Medicare is going to pay the bills up front. However, if and when you go after the trucking company, Medicare will have a lien against your recovery for what they paid out, and both the trucking company's insurer and your lawyer (if you have one) are legally required to reimburse Medicare before paying you anything. Same thing can happen with this bridge. The government can rebuild it now, and when the shipping company's liability is sorted out and adjudicated, the government can be reimbursed.