Couple things you can do:
A) Lazy load youtube videos, you do it the same way you lazy load images (reference: https://speedboostr.com/shopify-lazy-loading). This will help.
B) The best way, but a little more effort is to create a static image with a play button and load that, then set a JavaScript listener for click on the image and when that gets clicked, replace the image with the embedded video. I don’t have a tutorial for this one but just send that explanation to your developer, they should be able to figure it out. If you get stuck we have a service called Deferred Video Loading to solve that: https://speedboostr.com/services.
If editing yourself, remember to duplicate your live theme first and work off the new backup theme while you’re editing, so any changes don’t affect the live site + you can measure the before / after to verify you’ve done it correctly and gained speed.