How can you govern a splintered country, half of which think that you (the president) stole the election?
You've got more chance herding cats.
That's an interesting question.
Scott Adams once pointed out something called the "New CEO Move." It's when a new CEO comes in and immediately does SOMETHING so he can claim he did SOMETHING and it was good and supported by everyone. It's how you solidify support.
So how would a theoretical Biden with his marbles solidify his support after discovering -- lets give him the benefit of the doubt here -- that some overzealous antifa types went rogue and rigged the local elections without permission, causing him to win?
He'd need to immediately turn on his party. Not really, but he'd have to flee to the center -- a time honored DNC tactic, after all. He can't really throw the rogue elements under the bus, although that would be the best method to do so; The left is utterly reliant on stealing elections, it's one of the unspoken things in politics -- so he can't just say "yes there were some oddities and we're investigating."
But what he could do is say "I agree this was a very odd election and we need to investigate and ensure all Americans can vote if they want to, only American votes should count, and the vote counts should be open, accurate, and transparent." Does not accept blame or anything of the sort, and is just vague enough to get moderates and maybe even center-righties on board. Blunts the yes-it-was-rigged side's weapons.
Then he'd do a "New CEO Move." I don't know what that would be. Something that needs to be done, something obvious, something not controversial, but something he can get done and take credit for it. The trick would be that he'd need to do something so milquetoast that even the GOP won't argue against it. Ironically, an actual infrastructure bill would be ideal, but he'd have to keep the DNC's pork out of the damned thing. There will be time to embezzle funds later, after all.
Ideally he would throw the GOP a bone. Acknowledging that they're using a Trump plan would be a way to go, but that would require he break kayfabe and stop pretending Trump is the antichrist. But he could call it "the GOP plan" instead of the Trump plan, as a thought. "This Bipartisan Vaccine effort" or "The Afghanistan withdrawal, negotiated by our esteemed coworkers in the GOP..."
And of course, you need to get rid of the progs in this timeline. So the next time Antifa starts acting up, you nail them into the fucking GROUND. Unleash the FBI on them, tell them to actually arrest them -- not the sons and daughters of the DC and Journalist elites that are in Antifa, of course, nor the actual community organizer leaders, but the useful idiots are no longer useful, so they get to go to jail for the rest of your term. You let your RINO and GOPe puppets play up how Biden's based and redpilled because he's actually beating the shit out of Antifa in the street -- something Trump never did.
In short, he needs to be inoffensive, an effective leader, and toss just enough of a bone to the GOP that they'll begrudgingly think, if not say "well, it was bullshit that he got in, but at least he isn't fucking things up too bad, and we can just vote him out in 2024."
Sadly, he's a fucking potato brained pedophile who is the living avatar of his party's new "you either agree with us lockstep or it's hate speech, reee" mentality. So he literally can't do ANY of that.
I'm not political, so I'm sure there's a shitload wrong with the above. But if I woke up as Joe Biden Jan 20th, 2021 in some sort of wacky scifi comedy, that's the path forward I guess. Retreat to the center. Dial down the national temperature. Toss some red meat to the GOP. Do SOMETHING that I can claim as a victory. And start dealing with the Marxist Domestic Terrorists that the left has been using locally. And I'd keep my eye out for Pelosi, cause I'm 99% sure she wants Biden and Kameltoe dead. (Seriously, that Nuclear Football thing...)