Ash here from the Shopify team.
This is a great question! There are absolutely some themes in the Shopify Theme Store that have built-in product filtering. You can search through the available options, and check out previews of the themes by searching our theme store for keywords, such as "product filtering". Here are a couple options I found that may appeal to you:
Also, while I realize you ideally aren't looking to use an application, I do suggest taking a look at some of the options that are available. There are some free to use product filter apps that may be worth testing to see if they suit your needs. Here's a link to our App Store with a pre-filled search for product filter apps. I totally appreciate that you may not want to use an app, but I wanted to make sure you have access to a number of options before committing to a decision.