After finishing the first part of an adventure and leveling up, the party continued to the next part but all of them died. Now, we are trying the adventure again but without redoing the first part which would be tedious and time consuming.
On their way to level 2, the player characters found multiple items (like potions, equipment, or even items that are just meant to be sold). These items, even though they may have little value at higher levels, at their current situation may provide some much needed help in their adventure. But because the whole party died, all the items are lost with the dead party and I can't just tell them "Your new characters have the same items as the old ones had when you died before" as that would take away from the "immersion".
I know that there is starting equipment depending on class and I did see the answer in What's the starting wealth for higher levels?, but that's exactly my problem. The DM Guide says that starting at levels 1–4 they still only get starting equipment, but in this particular situation, I feel that the characters should own something extra
So is there a guideline to award each character with any sort of items or is it completely up to the DM to decide? Is there a more helpful guideline than the one in the DMG?