There's a couple of things worth talking about here.
If you're designing or building something with Shopify did you not scope out the costs of the platform into the work you're doing? That's risky and something you may want to reconsider for next time. It would have been rare for me to use a paid plan to build on, but it did happen occasionally and I made sure this was worked into my costings. You can try reaching out to Shopify to see if they would extend the trial but this would be at their discretion and may not even be possible for that shop.
If you have a Shopify Partner account you can make a dev shop. The purpose of this is to let you build proof of concepts before going live and handing it off to the client. Those don't expire. If you have not looked into those you should for your future builds.