It’s difficult to be specific as all companies follow a different process even though they may adopt a common model.
My history has always been starting from a product specification document originating from marketing or sales. Over years my involvement started earlier until actual release of the product specification document to the project team included select ID sketches and renderings. The design interpretation, critique and selection was done by a very small group, which worked well compared to other projects where there were more stakeholders and, usually negative or just inappropriate, opinions.
It was established, by the engineers of all disciplines, that having a mental image of what they were starting to design was a tremendous benefit, rather than previous finite specifications such as functional block diagrams and cost targets. As various engineering disciplines started I and other designers continued in communication with them to refine the concept with appropriate space claim, including models. Something I’ve never really done in this process is “hand over to the engineers”, always staying involved to some extent, often to continue to explain, fight for and defend everything from the entire design concept to minute details of button placement. A few projects where I have been less involved indeed the engineering team has been guilty of some pretty egregious redesign based on their individual finite work packages, and unfortunately in a complex world it’s the original designer , not the engineers, that gets asked why this detail is so bad.
I would include in any multi-discipline team design procedure the ownership of responsibilities, not time limited.