You can pass by the threshold with PowerShell, however i don't think this is applicable because we are talking about standard users.
What you could take a look at is creating something referred as "Happy Hour" in SharePoint, which is a daily window where the resource throttling is turned off and users can perform large queries against lists without any list view threshold and should be able to export to Excel.
What's important is that this can have a huge impact the servers and should be well considered before implementing. Once they have an exported Excel, they should be able to update the excel to get any changes made in SharePoint outside the Happy Hour window.
To enable this, head into
central administration >
manage web applications, mark the webapplication you want to enable a daily window and under the button
general settings, select
Daily Time Window for Large Queries and specify at which time it should start and how long it should last.
Or, learn them how to filter the data and create specific views so they only export the least data needed. Which hopefully is below the list view threshold.