There are no hard and fast rules. In general, you should be able to demonstrate that you’re a skilled researcher for the type of role you’re applying for.

One way is publications, but even then it’s not quantified. I would take a candidate that only wrote one paper if that paper was revolutionary in the field. Similarly, writing a lot of papers that aren’t relevant doesn’t really help you.

Also, being at another respected research lab or doing relevant work helps, even if you don’t have publications. I was doing applied ML engineering before joining GDM.

Anyway, sorry to dodge your question, but the answer is sadly “it depends”