I worked in 600 person scaleup in Europe with a similar strategy to what you describe. Office admins covered most of the process, a smart (and bought-in shareholder) lawyer spent a couple of hours a quarter reviewing template employment contracts and regulatory changes.

We we growing fast and our recruitment process was feeling the strain, so we got some in-house recruiters.

A few years later, a full-function HR team got created, but waiting that long and starting with goal-oriented recruiters (not compliance-cowboys) was totally the right thing to do: a culture of manager and employee self-service, good tooling and as little bullshit as possible is a beautiful and smooth thing.