I can absolutely build you a landing page in Shopify. Although, I would recommend WordPress because that way, if you want to expand in the future to a full on site, it would be significantly easier.
But, I can build out your page with modern, mobile-friendly design in about 7 days.
Just a few questions; will you provide content (text)? Is this for an app? If so, can you provide screenshots so I can build out visual content such as images to better explain the product?