We would like to track user sessions on a customer's app using the marketing cloud SDK, but after digging on the internet I haven't find a way to do so.
Is it possible?
Last Application Open and
Last Message Open are part of the Mobile Push data model. You can check the list of all available attributes by going to Data Designer > Mobile Push Data.
From the send reports, you can also have
Time in App when a Push notification is opened.
But if you are looking for more detailed session data, I would suggest that you extend the Mobile Push data model using custom attributes & tags updated directly from the App using custom code.