Online Store Charged Me Twice And Claims It Was Two Separate Orders. I Only Placed One And Only Have Confirmation For One. What Are My Options?

I'd rather not name the store because I don't think that's the right thing to do, but happy to share more details if it helps.

So about a week ago I placed a single order on an online store, standard checkout, nothing unusual but I got two identical charges from the same merchant within about 3 minutes of each other.

I contacted their support the same day and their response was that these were "two separate orders placed by the customer" and that both would be shipped. I told them I placed one order and have exactly one confirmation email in my inbox and asked them to show me the second order number. They sent me a screenshot of their internal system showing two orders under my account with different order numbers but identical items, identical address and placed 2 minutes apart.

I did not place two orders. I was on the page once, clicked checkout once and left. I have one confirmation email, one browser history entry for the checkout page and my cart was empty after the first charge went through.

I pushed back and they said my case had been "escalated to the relevant team" and that they would get back to me "as soon as possible." That was six days ago and I have heard absolutely nothing since.

The thing that worries me most isn't even the money at this point, it's that there's no clear path forward here at all. They won't acknowledge the charge was a mistake, they won't cancel anything, they won't communicate and their only suggestion was to refuse delivery on one package and wait for a refund that they haven't actually committed to in writing anywhere and from a company that can't seem to respond to a basic support ticket I have very little confidence that process ends with me getting my money back.

Is a bank dispute my only realistic option here or is there something else I'm missing? And does the combination of no proof of a second order plus a week of no response actually give me a strong case? Location: Texas