Can you try to remove the Samsung account and add it back to see if you notice any change?
Do you ever get any error messages when this happens? Does the Chrome browser act the same for you?
Can you load the phone into safe mode and tell me if Samsung Internet still closes out automatically? I just tested on a Note 9 and all seems fine both in safe mode and on it's own, but I unfortunately do not have a Note 10 to test on at the moment.
I just bought the note 10+ everytime i open the Samsung internet after 5 sec. It closes automatically and i keep trying to open but keeps closing, i cleared cache and force stop the app but it continues to do the same.
When you cleared cache, have you tried clearing data?
So this typically means you have an app or setting that is potentially causing this to happen. Can you remember anything specific that was downloaded or changed right when this first started happening?
All I did when I bought it is using smart switch to transfer from note 8 to note 10+ and Samsung internet was working fine on note 8 also I didn't install or add any new apps on the note 10+
When transferring over from the Note 8, did you bring over any of the apps that were installed on it or just stuff like pictures/contacts?
Alternatively, did you use a theme on the Note 8? When using smart switch it could have transferred over the theme which could be causing this to happen.