The following allows you to know when an Intune App installed if there are no log files generated by the install.
Intune apps have an associated GUID which is displayed at the end of the URL when viewing the app in Intune.
This corresponds to the GUIDs written in various places below here
HKLM\SOFTWARE\Microsoft\IntuneManagementExtension\Win32Apps
e.g.
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\IntuneManagementExtension\Win32Apps\OperationalState\00000000-0000-0000-0000-000000000000\c1872573-4036-4eef-9228-d6e932b2d9f9
"ExecutionStatus"="Completed"
"ExecutionTime"="05/01/2025 09:51:19"
"ExecutionType"="Install"
"ExecutionReason"="Default"
"ExecutionReboot"="Clean"
In the above example the app with GUID c1872573-4036-4eef-9228-d6e932b2d9f9 executed its installation at "05/01/2025 09:51:19"