Is there a way to set a timeframe for an outgoing chat message to automatically disappear?

We have gotten feedback from customers that the automated outgoing message interferes with their shopping experience. Currently it is set up to show a snippet of a welcome message, and I can clearly see where the CLOSE button is located directly above the chat, but I think quite a few customers are missing that and becoming frustrated. This is primarily happening when customers are shopping on their phones (we do not have an app, just a mobile website) We want to continue to use the snippet feature instead of just using the badge, so I was wondering if there is a way to set up a time frame to allow the message to show. For instance, can I say that it should pop up after 10seconds on the page, but then automatically close 10 seconds later if the customer has not clicked on the chat to engage.