Hey @Karen M! I'm not a UXer myself but can speak in general terms based on experience working with designers in different constellations.

At my current company, most designers try to always design with a mobile first approach. In practice, they basically create all wireframes and design drafts primarily for mobile devices, then move on to tablet and desktop. The most obvious benefit is that the interface becomes more well-structured; instead of designing for desktop and then retracting or reordering whatever doesn't fit in a mobile viewport, they tend to think more relevance-centered, resulting in less mind-boggling differences between viewports.

Can't really think of specific drawbacks, I'm inclined to argue that the mobile-first approach should be default (unless the majority of people using the interface you're designing are on desktop).

The biggest challenge is probably lack of experience working with mobile design; lots of designers have been working desktop-first for a looong time and for them it can be quite a big shift in mindset to start working mobile-first. But they should all just learn.