It seems plausible with some conditions
The location of the body determines its golden age in terms of Earth life. Earth doesn't have a billion years left (maybe not a hundred...). Mars might be a good candidate from 1.5-2.5 billion years from now. (As others point out, the organisms need to survive in the meanwhile, but there are some earthly organisms that seem like they might be able to make a go of existing sheltered subsurface environments on Mars, and only a proper experiment could prove otherwise!)
The length of time the life needs to evolve depends on how much it has to work with. If you send another planet a coronavirus it will never have life; if you send it one bacterium with 3 million base pairs it will take a long while to work something out - though with the machinery of protein synthesis, it is billions of years ahead of where Earth life started. If you send it a well balanced care package of tardigrades, lichens, and extremophiles (such as Deinococcus radiodurans) they should be able to arrange something faster.
How fast? Nobody knows. The Fermi paradox is that we don't see life all over the sky, and one reason might be that it doesn't get past some "evolutionary bottleneck". What that bottleneck is, nobody knows. Body plans of major animal phyla have remained rather steady in some cases, over half a billion years; but then again, sometimes they don't (human vs. sea squirt). The bottleneck might be a combination of ecological niche and evolution preserving a status quo within it, which might depend on what happens to the planet later. (Nobody knows if any dinosaurs were on the brink of becoming intelligent per Jurassic Park, or whether they ever would have)
There are little guarantees in worldbuilding. Even God seems rather disappointed with the results.