Congratulations on developing a finished product. Now for the hard part, monetizing it. I'm glad to learn that you are thinking big with the goal of distributing your product to the masses via a big box brand. Unfortunately, gaining their attention and trust isn't so easy. Still, there are certain steps you can take to help you reach your goals.
First and foremost, there must be evidence to suggest that you have proof of concept. While I understand that you developed the product because you believe there's a need for it in the market, there needs to be proof. The best evidence is to show that people are using the product and have paid money for it. It doesn't have to be tens of thousands of customers, but a large enough sample size to support the notion that market acceptance exists. Distributing the product to smaller retailers would be the best place to start. If you're deeply concerned about sharing your product with the public for fears of competitors cloning it, there are other ways to show a need in the market, such as industry research, surveys and focus groups to show the need. It's not the best evidence, but there's a chance that it might be sufficient when presenting to a big box brand.
I would also recommend that you create a list of big box brands that you believe would embrace your product. Once you have a list, then search through your professional network for individuals that are directly connected with business development contacts at these big box brands. Use LinkedIn and other networks to try to find the right person to contact. If you can't identify any direct or third-party connections, you'll need to try to gain introductions through conferences, events and tradeshows that the company attends.
Once you do get the opportunity to speak with the company, you'll need to be prepared to explain the product features, manufacturing process, costs, price, risks and market opportunity. The more facts you can provide with numbers, plus qualitative evidence suggesting market acceptance from customers, the stronger your case will be for them to agree to distribute your product. Be prepared to answer difficult questions you may not have thought of earlier. Could your product pose a risk to children if misused? If so, what can you do to mitigate that risk? I recommend you put yourself in the shoes of the people to whom you’ll be presenting. Then, think about what you would ask if you worked at this company and an outsider was presenting a new product they'd like you to distribute.
Lastly, don't overlook working with a partner or a professional that has specific experience selling products to big box brands. You may have to give up some equity and/or provide compensation, but if it helps you meet your goals, it can certainly be money well spent.