Insolent Neonate + Bridge from Below
When activating Neonate's ability (or any other ability with multiple separate costs) you can pay its various costs in any order. And yes, the order in which you pay the costs matters.
If you pay the discard cost before paying the sacrifice cost, then the Bridge will be in the graveyard at the time the Neonate dies, and will therefore trigger. If you do it the other way around and pay the sacrifice cost before the discard cost, by the time the Bridge hits the graveyard the Neonate is already dead, and there will not be any trigger.