Hi,
When you've got the Teacher role, you have an option "Send forum post notifications with no editing-time delay" with explaination "This post will be mailed out immediately to all forum subscribers". Technically, it's the "mailnow" forum string.
So i think all you have to do is find the related capacity, and allow it for your users.
After digging a little, searching for "mailnow" in mod/forum/classes/post_form.php, it seems you need to have 'moodle/course:manageactivities' capability for that, there isn't a dedicated capability...
Perhaps you can make a suggestion for that in the tracker, for the future.
Otherwise, you can set to 1 minute the modification time allowed before sending notification (maxeditingtime in security settings). But it will be for the whole Moodle site.
HTH,
Séverin