I used to deploy SPAs like this and I consistently had problems with cloudfront's cache clearing. Projects would not update for random amounts of time and at different times for different clients. I thought I was pretty good a trouble shooting stuff like this but over months of effort I could never get it to work update when I invalidated the cloudfront cache no despite trying many different approaches.
In the end I have switched to hosting on Netlify, which is easier to set up, not that I particularly care about that, but when I deploy my live site updates immediately.