I'd argue that they can't, at least on a short timeframe. Not because LLMs can't generate a program or product that works, but that there needs to be enough understanding of how the implementation works to fix any complex issues that come up.
One experience I had is that I had tried to generate a MITM HTTPS proxy that uses Netty using Claude, and while it generated a pile of code that looked good on the surface, it didn't actually work. Not knowing enough about Netty, I wasn't able to debug why it didn't work and trying to fix it with the LLM didn't help either.
Maybe PMs can pick up enough knowledge over time to be able to implement products that can scale, but by that time they'd effectively be a software engineer, minus the writing code part.