The trouble is that many manufacturers install their own calendar apps, and they are almost all called "Calendar". So I never make assumptions about what calendar app someone is using unless I at least know what device they have.
I did just enable notifications in the Google calendar app on my phone (I leave them off as I have other calendar apps that suit me better) and created a test event, but it did not produce the type of reminder you describe for me. This may however depend on the device, android version or other settings (e.g. I have a Pixel 2 running Android 11 with always on display disabled). But the Google app, in common with most Google apps, is very limited in what options it provides and I couldn't spot anything in its settings myself that looked relevant to this.