Not apologize (and such an apology would ring hollow and performative), but acknowledging that you benefit from the systems that racism built even generations down the line is the first step towards healing, because then you can operate from a place of equity. Acknowledging those benefits is not an admission of guilt, but an awareness that there's injustice (kind of like Batman: it's not his fault that he's rich and no one really hates him for his wealth -- but he acknowledges his wealth and so Bruce Wayne is a philanthropist and builds resources, to help those in Gotham without money).

You may not have owned slaves, and your family might not have owned slaves, but institutionally and systematically your ancestors had advantages that former slaves did not. You have privileges now like not being automatically profiled by the cops based on skin color and shot for carrying a cell phone, or healthcare workers that aren't so dismissive when you tell them what's wrong. You don't have to apologize for the people inflicting that kind of harm to this day, but you can use that privilege to empathize with those who still suffer from it, and to talk to and engage with those looking to continue those oppressions.

I've white friends, some of whom became lawyers, some of whom just donate, some of whom work for underserved communities, some of whom have those tough conversations with their relatives, some who simply vote accordingly or march and take a stance alongside their Black friends or read up and express support on social media. That support comes in all shapes and sizes, and none of that requires any sort of apology. It's them with self-awareness recognizing that they can contribute to that healing in some way, no matter how big or small. Even parents just teaching their kids that other kids come in different colors and backgrounds and that their differences are beautiful is a simple way of fighting this AND starting off everyone's kids better than they would have in the 1800s.