Yes you can make an e-commerce website without a CMS/open-source script but it requires a lot of skills, knowledge and time. It may cost you a lot to hire a developer to create this site of yours.
That project may take months to complete as an e-commerce website is very complex, especially with all the payment methods and their API's.
There are website-building hosts - e.g. Intuit - with drag-and-drop applications that allow you to be up and running with an online store within a weekend.
They even provide you website templates if you're interested...