We're getting into the semantics of what's meant by "company" here.
When *I* talk about a company, I mean a company as defined in the Law of England and Wales, and specifically, the Companies Act 2006, the full text of which is here:
Companies Act 2006 (c. 46)
These are organisations registered with Companies House.
Now it's quite possible, in the Law of England and Wales, to have a very substantial firm that isn't technically a company. Firms of solicitors are a good example.
It's also possible to have a company with shares that haven't yet been registered or distributed by means of share certificates. But the shares exist, or are deemed to exist, unless it's a company limited by guarantee.
A commercial organisation of another kind isn't technically a company, though it might be a firm.