My name is Lilith, I'm on the Social Care team at Shopify.
At the moment there is a fantastic feature in your Shopify built theme that will allow you to do this. It won't remove the cart page from your site, but what it'll do is let customers click a "Buy Now" or dynamic payment button to check out right then and there instead of needing to view the cart page.
The feature is the dynamic checkout button. It can be turned on by following the guide in the link there.
The buttons that show up will depend on the customer's browser and device. For example, if a customer is using an Apple device and has Apply Pay activated on their Apple account, they can checkout immediately with their Apple Pay without needing to view the checkout page.
If a customer doesn't have any virtual wallets like Apple Pay or Google Pay, they'll see a Buy Now button instead that will get them to the checkout and bypass the cart all the same.
Here's an example of what those two possibilities may look like:
Be aware though that, this would mean that your customers can only buy one item at a time instead of multiple different products. That said, they will still have the option to add more to their cart if they aren't ready to just buy one item.
Let me know how you do with the information above! I'm happy to answer any questions you think of as you work on your business.