I know very little about this time period or this region, but it seems clear enough that they need to prevent that Silla-Tang alliance somehow. Fighting on two fronts, with one of those fronts being a state as powerful as China could only end disastrously. Perhaps if they'd been able to bide their time and strike at Silla while the Tang are distracted somewhere else, they could deal with the threat in their south and then figure out a long-term solution to the Chinese threat. Some sort of tributary arrangement might be necessary, and I'd imagine that they'd likely lose some ground to the Tang before they accepted the necessity of doing so, but if they could pull that off, then I don't see why they couldn't more or less rest easy at that point, and probably absorb Baekje at their leisure.
And in the long run, so long as they avoid getting colonized by outside players later, I don't see why their dynasty or a successor couldn't survive to the modern day. And honestly, even IOTL you could argue that Goryeo was a successor to Goguryeo, and Joseon was a successor to Goryeo, so any timeline where Korea avoids annexation by Japan and keeps its independence would fulfill that condition.
