Can I bypass password on a refurbished Mac mini?

To be honest, you did not buy a refurbished MM, you bought a USED MM. Moving forward it is unwise to buy used Macs from:

• Ebay
• Craigslist
• Marketplace
• Nextdoor
• Local PC Shop
• Friend, Neighbor, Relative etc.

Why, simple more often than not the computer was NOT setup correctly for resale and you are only inheriting someone else's problem. Macs MUST be setup correctly otherwise the buyer will have trouble, just like you are having now. The computer will ALWAYS be associated with the original owner, it should have been setup per Apple's directions in What to do before you sell, give away, or trade in your Mac.

Moving forward, you can buy genuine refurbished Macs directly from Apple. These are identical to new, have the same 1 year warranty as new, are eligible for AppleCare and can save hundreds of $$. You can find them on Apple's home page (www.apple.com), scroll to the Botton and click on Apple's refurbished store.

If a genuine Apple refurbished Mac is still too expensive for your budget, contact a reliable reseller such as macsales.com and you can get older Macs that are setup correctly and also refurbished with high quality parts, unlike your Ebay machine.

If the previous owner parted with the Mac willingly, they should have done this:

What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

If the Mac shows signs of not being prepared and the eBay seller is giving you the runaround, that is a red flag. Return the Mac for a refund, if you can.

You may also want to read

The All Too Common SAD Reality of Buying a Used iPad/iPhone – Apple Community

Although that User Tip is written with iPhones in mind, some of the advice is also applicable to Macs, especially recent ones which support Activation Lock.

There is no workaround. Apple will not help. Return it to the seller for a refund. It is likely a stolen device.