How do we find new businesses that need packaging and fulfillment?

The fact that you are looking for "new" businesses makes this a bit challenging. Direct mail seems your best bet. 

On a local level, you can obtain lists of businesses that have just incorporated or registered in your area. And on a national level, these lists exist as well. You'll need to find the right kinds of businesses on those lists, however, possibly based on some assumptions drawn from their SIC codes. 

I suggest you contact a reputable list broker rather than try and find these lists on your own. List brokers are independent businesses that are generally compensated by earning commission from the list vendors, so it may cost you no more--or possibly only a small fee--to be guided by a professional.