At the moment there's no option to trigger the Messaging widget to pop up after a minute. But, you can work with your developer to keep the widget open. You can provide them this developer documentation API that you can add to the Messaging snippet code to keep the widget open:
<script type="text/javascript"> window.setTimeout(function() { zE(function(){ zE('messenger', 'open'); }); //You can add more APIs on this line }, 10000); //time’s in milliseconds - 10 seconds = 100000 </script>
At the moment there's no option to trigger the Messaging widget to pop up after a minute. But, you can work with your developer to keep the widget open. You can provide them this developer documentation API that you can add to the Messaging snippet code to keep the widget open:
Web Widget API
I hope this helps! Thank you!