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No problem. Any fit cyclist could do a 10k in a bit over an hour I think, assuming they don't get themselves injured, without any training. If you want to do it reasonably fast or without having to rest your legs for a few of days afterwards then that will take a bit of training but you can easily do it in 20 weeks. For comparison most marathon training plans are shorter than 20 weeks although they assume that you already do a bit of running.
I'd bash through a training plan in 8 weeks to get your fitness up and then focus on getting as fast as possible for the next 12. Plus you have loads of spare time if your training gets delayed for a week because of life.
Runners of LFGSS, 20 weeks to start from scratch to running 10k? Doable? I've got a decent fitness, allways warm up on crosstrainers before lifting, cycle everyday but the last time I ran more than 5 minutes is a couple of years ago. Colleague is trying to rope me into running an Urban trail with her.