Hello,
Normally, if you've configured Internet Connection Sharing (ICS) to share an internet connection, it should persist through reboots, and the shared interface should be automatically re-established.
You may check the "Internet Connection Sharing (ICS)" service is set to start automatically and check for any startup delays. ICS may also depend on other services to function correctly. Check if there are any dependencies or related services that might not be starting as expected during the system startup.