Initiate add-on install from 3rd party application

Would it be possible to prompt a user to install an Atlassian Connect add-on on the Atlassian marketplace from within a 3rd party application? The intention is to be able to link the Atlassian product with our own application’s tenant information for that user.

Simply linking the user to the marketplace would leave our application with no way to correlate that installation with the user account that requested it.