The vast majority of our hiring is for DC roles, because that's where the work is for us. 1-2 of our agency partners let folks come to DC for 6-12 months, then have a conversation about remote work. But it's helpful to come to DC to get a handle on how the government operates... differently than the tech industry.
We did just hire a recruiter who is based in SF, but it's mostly DC for USDS.
We are definitely looking for product managers, along with software engineers (e.g. backend, frontend, SRE, data science, security, cloud, API design) and designers (e.g. UX research, service design).
For product marketing, the closest role to that might be content strategy, which has proven quite useful.
We don't really end up building many apps, so you're probably better off finding a closer match to your interests/skills. Sorry to be the bearer of bad news!
We did just hire a recruiter who is based in SF, but it's mostly DC for USDS.