Lambda@Edge to configure SPA client side routing? (ReactJS) S3 + CloudFront

My website is a static site in S3 and I'm using CloudFront. Since it is a SPA , the origin returns a 404 error on every request but loads the page successfully. To solve this I have created a custom error in "Error page" in CloudFront so that it returns a status 200. (This is what is recommended in most blogs) This works fine but on every html request I see cache: "Error from CloudFront".

My question is if CloudFront is caching the request or is it always going to the origin? Would it be better to handle this with a Lambda@Edge? How?

Thanks in advance!