I understand what you are saying, but why does the time matter? For a lot of notifications such as likes or badges, it’s kind of irrelevant to show a time. I know you’re on mobile but on desktop, if you view all your notifications, you can hover over the time for more precise information.
As Jakke said, Discourse isn’t the same as Facebook or other social media platforms it’s meant for asynchronous discussion. For example, when I open Meta I check my notifications and have a gander in my own time. I don’t suddenly drop everything (a bit of hyperbole here 
) after I’ve seen a notification from merefield replying to my post, thinking, omg, I have to reply now.
Perhaps your desired outcome could be achieved by a theme component?