As I understand it, there is little belief that life could have originated on Earth until the end of the Late Heavy Bombardment (4.1-3.8B years ago) but DNA-based life was certainly established by ~3.4B years ago. I was taught that DNA-based life was certainly preceded by "RNA-world" and that was most likely preceded by some kind of protein-based system. So you've got ~500-700M years to bootstrap all the way to DNA.
But now it appears that "slow meteorites" might transfer from solar system to solar system, opening up several billion years of additional chemistry experiments. But on the other hand requiring chemicals coming from compatible planets and surviving several million years of hard vacuum and surviving falling to Earth and somehow taking hold...
Is it reasonable to be skeptical that ~500-700M years is enough time for abiogenesis? Is that timeframe considered a "problem" by scientists?