Starting a coding project just to improve a job application

Starting a coding project just to improve a job application I am applying to a software engineering job where I don't check all the boxes. A missing box is important, not decisive on its own though. I thought I could do a very small project around it and share it with the hiring team, to prove I can build what they need anyways. However, that would require investing significant personal time before even knowing if I would be considered. The company is small and applications are done by writing to one email address, so I think there's no ATS of sort, and given their career page I think they will take a look at the repository. I otherwise have 3 years of quite relevant work experience, but no recent projects to share given IP constraints. Do you think it's a good idea to do this project? Won't they ask me to do something like this during e.g. a coding homework for an interview if they decide my CV is good enough? A weekend coding project won't make me proficient in that skill anyways.