I wouldn’t recommend doing that, giving away your core product wouldn’t necessarily be a good idea. It’s best to first figure out what distribution channels would work best for you and your business. Since you are interested in shipping and selling to the USA then your first order of business would be to get in contact with a freight forwarder that would assist in bringing your products to the country itself.

After you may want to try to list your product on E-commerce marketpalces that facilitate business for non-us residents like Amazon and Ebay and making efforts to make sure that your listings are optimized for SEO so people have a higher chance of finding them. Amazon FBA would be a good place to start since many people trust products fulfilled by Amazon.

If you can get those two things working you should be able to ramp up on your sales and where necessary you can include ads and posting on organic sites to drive more traffic to your products but giving the sample away just because there are no sales now wouldn’t be the best idea.