I can't imagine how some of the responses have not helped pushed this to the next stage already.
Anyway...taking a stab at this. Hope it isn't a waste.
With some villain protagonists, it is easier to get sympathy for them because you can just turn up the sympathy bar by making their life hell. It's easy to make somebody root for the terrorist mastermind who lived in 3rd world squalor and saw his parents gunned down by western soldiers, for example.
Not so easy if nobody really gives any about the character. Tragedy after tragedy will not automatically elicit sympathy from readers.
Have you made any progress with this character in terms of finding out who they really are? How do their minds operate? How do they rationalize the situation before them? How do they warp reality in order for it to suit their own worldview?
What are some of the very human qualities you can pull from their evil intentions that speak to desires we can relate to? Don't work on the assumption that some of the most corrupt thoughts are totally inaccessible to others.
Not having the restraint that others have means that your character being who they are may not be as much of a barrier as you think. You can use it to your advantage. Some might not like to think unkind thoughts about the good intentions of others (desperate to be liked, people-pleaser, doormat), even if these qualities are embarrassingly obvious, but your character may think on these freely and how they may use it for their own ends. And people may very well be able to connect with that impatience or disdain for overly-helpful types or whoever else, even if it is not something they're open about.
....is a murdered family(and possibly friends + LI) enough "pain" to get readers to sympathize with them a bit? Or would you need to crank down the severity of their flaws at the start to make it work?
I think you need to change your focus entirely and stop looking for the one guaranteed thing that will conjure up feelings of sympathy, like magic.
There isn't a pitiful enough backstory that will make a reader want to connect with them
in spite of their quest for revenge and great power.
Maybe just go with it. Delve into their psyche. Get lost in their twisted logic, the world as it is through their eyes. Turn their minds inside out and expose it to us. For the all the world cares, they appear as nothing more than a spoiled brat. Is that really all there is underneath as well?
The goal shouldn't be to give readers a "oh well, he's had a bad life so that explains it" reaction. That's attempting to minimize what the character does, to not really have to deal with their actions and the consequences of it. It's trying to have a special reason to point to constantly and say, well this is why this happened. They're damaged.
They would not see themselves as terrible. They do not feel they have to excuse their actions, and you should not have to write one for them either.
Maybe they could even be the kind to "give back" but more out of a desire to maintain a good public image then any kind of genuine concern for the less fortunate?
Unintentional acts of kindness won't do anything to put them in a softer light.
Although,
Such acts could be a springboard for glimpses into how carefully your villain crafts and maintains their image. Every perfectly timed smile to the crowd, hitting all the right notes in a speech for some cause.
That might in turn lead to us being able to see some all too human cracks here and there in the highly-polished surface.
It may feel cliché, writing a two-faced bastard, but the right kind of language and imagery can evoke an all too vivid picture of what it looks like when a human being pushes themselves to their extreme limits, someone who exerts every ounce of their energy into playing the part of someone they absolutely hate, of someone everyone else wants to get to know better. And all of that strain only a small part of something so much more complex.
How badly does your character want it? What do they risk losing? The reader can be there with them in the moment, on tenterhooks, if the scene could be crafted just so.
Some may still not be into it. Some may want to stay for the completely mind-boggling determination and amazing endurance.
And this isn't to mention all the other qualities that you've not yet explored. Maybe once they've all been pieced together, you'll have someone, however selfish, readers will want to care for because of the life that's been breathed into them.