Connect with the CEO of 3 non-competing products that already sell to those stores and ask them for advice on the process, the people involved and things to consider.
That's always the fastest way in my opinion.
I hope this email doesn't come too late... As a former retail buyer for Target, the best way of getting your product into stores is by focusing on telling the story of how your product benefits the retailer's financial and business goals. Most product companies focus SOLELY on how great their product is. But you know what? There are tons of great products out there. Retail buyers are not in short supply of great products. So to really differentiate yourself and pique the interest of retail buyers, you need to wow them with sales history. Knowing how your product sells in other stores (the more well known the store, the better) gives retail buyers a sense for how your product might perform in their stores. And sales potential is what really excites buyers. Additionally, telling them how you are growing brand awareness, creating demand for your product and your ability to funnel traffic into THEIR stores will be even more compelling. Focus on telling retailers how your product benefits their revenue and margin goals and how no one else can do so as well as you - and you'll be prime for getting your products in their stores. I'm happy to do a call for follow up questions.