You can turn the Convert tracking script into an async one by adding the async attribute to the tag itself.
Disable Body Hiding
Also, before the main tracking code you would need to disable the body hiding as otherwise it will cause a blink on every page load as explained at https://convert.zendesk.com/hc/en-us/articles/205160025-Disable-Body-Hiding-in-Convert-Experiences
Install Modified Tracking Code
The final tracking code would be something like:
var _conv_prevent_bodyhide = true;
<!-- begin Convert Experiences code-->
<!-- end Convert Experiences code -->