Unlikely. See my longish comment above how ~ 30 000 years is now known to suffice until cellular ancestors arise. They only need 2 individually self-assembling and spontaneously replicating components, liposomes and the thermodynamically driven crystallising RNA replicators. For example, Mars with its mere ~ 3 million year until accretion got a head start on Earth with its ~ 30 - 300 million years (latest core formation theories) had an impactor tramway of material raining down on Earth as it formed. Calculate cellular mass content of average crust and its survivability under launch impact and shortest route to Earth (all researched and published, thankfully). Even if the martian tramway delivery rate was order of magnitude larger than today's ~ 200 kg/year estimate, you don't get the average delivery rate of 1 (one) surviving cell up to the above abiogenesis rate. I don't think we can reject the possibility at 3 sigma, but the simplest pathway of "in-house assembly" is the superior at 1-2 sigma. As for incoming life at later times, we don't see it in mass sequencing. Indeed, it would have a hard survive will already adapted life makes lunch out of it.
? Bacteria has sturdy cell walls as ancestral trait (cf mycobacteria who lack it), eukaryotes with nucleus have only membranes.
In fact, the original (parent) usually ages as we do, as its continuing "half cap" membrane + associated cellular machinery will accumulate cellular damage and die after some ~ 200 divisions. (Seen in some experiments on modern bacteria.)
Bacteria has a lot of interesting sexual (or sexual like) traits, like sharing chromosomes by way of membrane tunnels. So something like it has evolved many times over. But evolution doesn't use "hopeful monsters" (macroscale mutations), but proceeds mostly along darwinian pathways: small, survivable, on average fitness increasing steps. (See near neutral genetic drift and genetic bottlenecks for variation driven pathways.)
Another inadvertent anonymous posting.
I never noted that I posted that anonymously. Silly me. But now I'm a slashdot trainee.