If I designed a new product and began selling it without a patent in the United States, then other suppliers copied the design and began producing the design commercially before I filed for a patent, then I filed for a patent and was awarded the patent, can someone later say that I should not have been awarded the patent because my product was commercially available in the public market and therefore prior art? I'm wondering if someone might try to invalidate my patent.
35 USC §102 spells out the criteria for what counts as prior art in the US. In the case you've described, where the invention is first disclosed by you (e.g., by your sale of the product), then others' sale of a product using the invention would not count as prior art for your patent, as long as your patent application is filed within 1 year of the original disclosure (see §102(b)(1)(A)). This is true whether the other suppliers copy your design or come up with it independently.
However, if you do not file the patent application within 1 year of the original public disclosure, then that public disclosure will count as prior art. Also, most foreign jurisdictions do not offer this 1 year "grace period", and so your own sale of the product will count as prior art outside the US.