Building a product without defining an ICP

The product was originally built for one ecommerce business with a very specific (and pretty broken) support workflow. They weren't using a proper helpdesk, so I designed the whole product around how they actually handled support.

now I want to introduce it to public and grow beyond that specific use case.

the plan is onboard the original business and get them actively using it then

• Ship enough features that it feels like a usable tool rather than just an MVP.
• Get detailed feedback from the original business and iterate.
• start doing cold outreach and marketing and narrow down the ICP.

rn ICP is basically just Shopify store owners.

It's my first time ever encountering this situation so would love to hear your advise