I own a startup and a supplier I'm doing business with for the first time has required full advance payment before they start manufacturing.
I have received a sample and it covers my requirements.
I've done due diligence on the company.
How can I get protected in the case of any problem we might have with the order?
Depends which countries we are talking about. You need should definitely have a written contract, and if possible, negotiate for a security deposit arrangement.
Legal remedies are your best bet - a written contract is essential.
It's nice you've done a due-diligence investigation, that's important before any payment options.
For custom products, a common practice of payment is to pay some upfront(20-50%) and the balance against shipment. This is fair to both seller and buyer.
If your order is small and the supplier is very strong, the mentioned requirement of full upfront is understandable. You can still negotiate the partial upfront term with them.
Zero upfront could hardly be accepted by supplier for custom product, as the goods are for your only. If you don't pay, they loss much.
If you still feel hard at talking payment terms with them, try to start as small as possible.
Beyond cash payment, you may also consider Letter of Credit. It is a bit more complex but widely accepted in trading. Basically it is document your bank issued to supplier's bank, guarantee that you will make payment after the supplier rendered right documents(shipping receipt, inspection report etc). Letter Of Credit could also help you on cash-flow, you don't need to pay cash right away. This option is good for long term supplying, and may be a bit complicated for first time trial order.
Full up front payment from new business or new clients are common and understandable practice.
If you are afraid for the honesty of the supplier I would suggest using services like PayPal, which allows disputing payments for up to 45 days. This will protect you from bad sellers and sellers from you, while your credit worthiness is established.