My iPad mini that I purchased at an estate sale is locked. Is there any way I can activate it?

tl;dr No.

You need the AppleID and password used to initiate the Activation Lock.

Here is a link to Apple information about Activation Lock:

Activation Lock page: https://al-support.apple.com/#/getsupport

There is no workaround for the security features of Activation Lock.

Please read this article before considering the purchase of any other used Apple device. Best to be forewarned.

The All Too Common SAD Reality of Buying … - Apple Community

The most important part is this:

... if it DOESN'T OPEN TO THE HELLO PAGE, OR SET UP PAGE FOR APPLE WATCH, WALK AWAY. An iPad or iPhone which has been prepared properly for a new user will ALWAYS open to the HELLO PAGE when turned on, followed by setting the language and then the set up assistant will walk you through connecting to a Wifi Network, following all the way through setting up the iPhone/iPad as your own. An Apple Watch, which has been prepare properly for a new user, will tell you to place the watch near your iPhone to start the pairing process. If it doesn't, you can't use it.

Apple, Staples and perhaps BestBuy will recycle the iPad for you.

Many local governments also offer recycling for electronic devices.

the owners family may be able to salvage it

How to request access to a deceased family member's Apple account - Apple Support

You might also investigate its return for a refund. It wasn't in a fit state to sell as a second-hand device.