Us Mint Denied Claim For Misdelivered/stolen Package And I'm Out ~$3,000

In November 2025 I purchased a gold coin from the US Mint worth close to $3,000. USPS tracking indicates it was signed for by "D DFDDF" (obviously not a real name) and I have not received the package. I live alone. Not sure if the mailman stole it and then signed a fake name or if it was misdelivered to someone who didn't want to sign their real name. As soon as I realized my package was missing, I immediately submitted a Certificate of Non-Receipt (which is their official process to deal with this) and they replied back that they will need 4-6 weeks to investigate. After not hearing back for 8 weeks I sent a follow-up email asking for an update and they informed me that "Unfortunately, our records show that the order or item was received on 12/XX/2025. As a result, your claim was denied."

This is the first time I've ever had a problem with the US Mint. Should I submit a chargeback with my credit card? After some internet searching I have seen that others who have submitted a chargeback for US Mint orders have had them come after them with threatening letters that they are going to send their "debt" to collections. I know that I could potentially fight any negative remarks on my credit report but I'm considering buying my first house soon and I don't want this situation to interfere with that.

I'm really upset about this and don't know if I should submit a chargeback with my credit card company or talk to a lawyer. Should I go to the post office and inquire about it? This is a lot of money for me to lose.

Any advice would be greatly appreciated.

Location: Arizona, USA