Panspermia posits that life started in one place and expanded from there. "There" would have be very near "Here" for that stuff to just drift around in space until it found a suitable environment. Now, given that life appears to have started here very early on, and probably died off several times before the planet settled down, the coincidental timing is extraordinary.
If we get out into space and "panspermia" particles are floating around everywhere then this might be likely, sorta. But if that original life didn't start in this galaxy then the odds go down drastically. Random radiation of particles would require huge amounts of them to accidentally land here. Also, if that original life source were a good ways away it wouldn't be here yet unless there's some mechanism we don't know about in action.
If we get out into space and "panspermia" particles are floating around everywhere then this might be likely, sorta. But if that original life didn't start in this galaxy then the odds go down drastically. Random radiation of particles would require huge amounts of them to accidentally land here. Also, if that original life source were a good ways away it wouldn't be here yet unless there's some mechanism we don't know about in action.