They were excited that they had started. They knew they still had to run it by the Coach, but at least things were moving.
the next sentence:
They had just employed their first full-time employee and felt as if a huge load had been lifted off their shoulders.
If they're publishing manuals and are a start-up company, there will be many issues to deal with -- getting an office, equipping the office, setting up communications equipment, ordering raw materials and printing (or having these things done), writing and proofreading the manuals, establishing pricing and shipping and customer service procedures, etc. -- so if these things are falling into shape, they are coming together in an orderly, workable fashion.
Imagine the pieces of a jigsaw falling into place to create a recognizable picture. Personally I think falling into place and getting into shape are the usual expressions and this is a mix of the two. There is also coming together, just to add to your list of similar expressions.