In the USA, it is possible for an LLC to buy wholesale without paying sales tax and resell the items (including exporting). To do this, you will need to apply for a Reseller Permit, which is free and requires you to fill out a form declaring your intent to resell wholesale items each year.
It is important that you declare the wholesale items and sales of goods on your tax return and are transparent about the overhead costs, the markup and the profit. Stores can (and will) require you to show your Reseller Permit prior to selling goods for resell purposes, especially if they are tax exempt. However, many wholesalers will happily provide you with discounted products void of sales tax once you show your valid permit.
As far as I know, reseller permits expire each year and must be renewed by the Department of Revenue website for your state. Each state's rules may vary on this. Although you can purchase items for resell tax-free, you must charge sales tax on the final product and you also must pay taxes on all profits and sales you make.
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(Disclaimer: This answer is for informational purposes only and does not constitute financial, legal or other professional advice. Use at your own risk, we will not be held liable for the accuracy or use of this information. When in doubt, consult a licensed accountant for specific tax advice).

The ability of a registered LLC to purchase goods in bulk from an online platform and export them using tax exemption will depend on various factors, such as the nature of the goods, the tax laws of the jurisdiction where the LLC is registered, and the tax laws of the jurisdiction where the goods are being exported.

In general, LLCs may be able to purchase goods tax-free if they are purchasing them for resale. This can depend on whether the LLC has a valid reseller certificate or sales tax exemption certificate, which may be required by the online platform or seller. However, if the LLC is exporting the goods, it may be subject to export laws and regulations, which can vary by jurisdiction.

It is essential to seek the advice of a tax professional or attorney who is knowledgeable about the tax laws and regulations that apply to your specific situation. They can help you navigate the complex tax laws and regulations and ensure compliance with applicable laws and regulations.