I suggest you check senitnelhub-js library:

GitHub - sentinel-hub/sentinelhub-js: Download and process satellite imagery...

Download and process satellite imagery in JavaScript or TypeScript using Sentinel Hub services. - GitHub - sentinel-hub/sentinelhub-js: Download and process satellite imagery in JavaScript or TypeS...

You might even check how this is done in our Sentinel Playground, it’s open-source:

GitHub - sentinel-hub/SentinelPlayground: Simple application for using...

Simple application for using Sentinel-2 WMS service - GitHub - sentinel-hub/SentinelPlayground: Simple application for using Sentinel-2 WMS service

Here are also two small demo projects

• 
  project using sentinelhub.js to get images and display them as <img> DOM elements


• 
  project using Process API to get images and put them on a Leaflet map and Catalog API to get the dates (without using sentinelhub.js)