Hey Ns,
Thanks for reaching out. There are a couple things to check. First, try the Shopify pixel helper and confirm the pixels are subscribed properly to the event. Second, if you see a green dot in the shopify pixel helper it indicates that the call back ran correctly. Third, you may have a top level error in your pixel code that stops the pixel from running in some cases. Shopify is working on providing runtime error reporting for each pixel but in the meantime, let me know the shop and pixelID and I can pass that along to the Shopify team to take a look.
3-7 seconds is a large delay so I would recommend having a look at what else is loading on the page before the custom pixels and if that can be optimized. On the new Thank you page, you will not see this issue because web pixels would have initialized when the checkout was initiated.