Keep in mind Udemy is already doing this for many courses. That is a big part of their business model, to do lots of advertising. So you might want to look at what kind of ads they are already running for similar courses (there are some tools that can do that, like spyfu etc)

Here's a guest post I wrote a while back talking about Udemy and how it fits into an overarching marketing strategy (like for example how you can have a free course that gets 10k students, promote your paid course to those students, and overall focusing on using udemy as a lead source to grow your main business)

https://docs.google.com/document/d/1GTk2DvSfKM-a9h4hRW4JtM9DkMGwDmV1yweWUEklbDo/edit?usp=sharing

That should give you some great ideas for where to start with this.

Had to share the google doc version because it looks like they migrated their blog when the company was acquired :)
(was originally here - https://wpcurve.com/online-courses-to-build-your-business/)

Hit me up if you want to talk course strategy / course marketing strategy - would be happy to help

Here's a case study that goes deep into course marketing with one of our clients (it's not about udemy, but should give you a clearer idea of the bigger picture with respect to how to market courses)
https://monetizemyexpertise.com/case-study-cloud-living

Take care,
Grant