It's agreed that Frisk becomes stronger when they have higher DT, which is how they're able to fight with Asriel in the first places. Even with a LV of 1, and while using the Stick, you can still deal plenty of damage to Asgore with all of your attacks. The reason why you can damage Asgore at LV 1 with a Stick but not one shot extremely weak Monster's like Froggit with the same things is very likely because of Determination, which makes further sense as there's even narration stating that you're filled with Determination right when the fight begins. Sure, there's no direct evidence that they specifically got stronger with Asriel as well, but due to the fact that their DT makes them stronger even in less extreme circumstances, it's not far fetched at all.