You can ask them to sign a contract now, and while you are waiting, and perhaps inform them you have to stop all work until the contract is signed. But then you might also lose the whole job.
You can also ask them to pay at different milestones of the project. Make the milestones, and the amount they owe, crystal clear. Then if they miss a payment, you will know they are not serious about paying you.
A professional should have thought about this at the very beginning, but live and learn. These things happen and there is a cost to them. Let's be honest, your oversight is not their problem.