Cut the tree down with the sturdy spear! No danger of breaking, I guess. If it breaks, we've always got more sap. Sap is now an universal problem solver.
The stress caused by the blow required to cause damage would overpower and shatter the spear, due to the length of the shaft.
I had the brief idea to make an entire shaft out of sap and just plonk a rock at the end. It is a silly idea. We must do it at one point.
But since that's impossible, what can we do with the spear? Would cutting a thick branch be doable if we did it carefully? Because a thick branch would probably be a better shaft than whatever stick we have for a handle now, and from there we can just hammer another sharp rock, combine sap, grass, the branch and said rock, and have something like an axe. Do we have any fireproof container, or materials to make said container out of? What are the trees around us, in the first place? There surely is something akin to maple around, but what we're looking for is white birch - so we can shamelessly peel all the bark it has and process it into rope, baskets, whatever else. From there, we can use the ropes to create traps, but from what I'm writing here it seems that's a long time from where we are now.