Your explanation of your product/service sounds like a medical device. Assuming that is true, your company is surely registered with the FDA and is audited by them every two years or so.
The comments in this list about federal law requiring a quality system *including software quality procedures* are correct. There is no way out of this and the company has a tiger asleep in engineering. The reason the omission has not surfaced is that FDA's budget has prevented them from auditing deeply enough - yet. They haven't been able to send auditors with enough software background to be able to detect the absence of the expected levels of software QA. They definitely have the qualified people, just not enough of them.
An additional reason could be that the product/service has not hurt anyone, or if so, the incident(s) have not been reported - which is another federal law incumbent on the manufacturer AND the hospital/clinic/doctor. FDA audits and warnings can come any time if enough of these reports stack up. Or if the docs send them in and the company does not.
Even if the code is really good and no medical problems have come up, that will not stop FDA from pulling your product off the market if they find you non-compliant with their regulations.
So the company has 'enjoyed' a prototyping phase. Once the management has read the FDA regulations on the personal liability of the company officers, they will probably want to get started with the formal software QA system right away. It doesn't have to be completed overnight. But when/if FDA look deeply enough into your company, you would want them to find records of your diligent work in building up the software QA procedures and practice in an ongoing and steady way. And doing the right things first.