Route 53 with Amplify and RDS: Host zone with custom IP address

I recently purchased a custom domain through Route 53 to use for a NextJS app that I’m hosting through Amplify, connected to a Postgres database in RDS. I haven’t yet configured the custom domain with the app - I’m still using the "Amazon-assigned" url. My question is this: is there a way I can configure a host zone with a custom IP address that I can use for the domain in order to connect "privately" with Postgres (in other words, to be able to assign a fixed IP address as an inbound rule to Postgres). If not, what are the recommendations for securely connecting an Amplify app to RDS - without adding a Lambda API layer. If the answer is to scrap Amplify and use an EC2 configuration, are there any simple step-by-step guides for doing so? Thank you.