It is generally possible to set such a cookie value in a LoadComplete scenario. For this purpose, you'll need to learn the logic of the script which sets the cookie, implement a similar logic using a bunch of Set Variable Value operations and set the cookie using a data replacer in the target request.
According to my knowledge of your framework, you have a more specific task - you need to generate epoch time based on current time and pass this value to a cookie. This is not supported at the moment.
Please let me know if my interpretation of your feature request is wrong.