Is this a button you’re expecting a user to click to indicate they’ve read a message?
Rather than relying on the user to do that, you could probably set the timestamp as part of the action when the user opens the chat.
The only way you might be able to do this is with some CSS, but that requires at least a Business Plan, and I’m not even sure it would be possible.
If it was me, I’d probably incorporate the counter into the chat image using Cloudinary. You could dynamically stick a liitle counter in the upper corner of the image. There is a bit of a learning curve with Cloudinary, but it’s well worth the effort.