The most common issue is having a shipping address that is not included in the shipping zone. You mentioned that you are using a third-party supplier so my first suggestion would be to reach out to them directly as it sounds to me that rates for weight and/or to some countries may not be set up correctly.
Share the name of the third party supplier so we can provide instructional guides to help with the setup
Some suppliers automatically assign products to the right shipping profile when set up correctly
TIP:Communicating shipping speeds at checkout to your customers can help improve cart conversion, provide clarity and transparency, and increase consumer confidence. Have a read ofthis blog postthat goes over shipping strategies to increase conversions and profitability for your business.
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