I just downloaded LibreOffice v7.2.4 to update v7.2.3.2. After I launched the installer and installed it:

I overwrite older LibreOffice installations with the updates, so the following panel appears where I select Replace.

and it proceeds to install LibreOffice:

Once it is installed, you can unmount the installer icon on the Desktop by right-clicking on it, and

Next, I right-clicked on the LibreOffice icon located in my /Applications folder and chose Open. This popped a dialog, and I clicked Open in it:

and for me, LibreOffice just launched. You would do this right-click on the LibreOffice application icon once per update, as this is all that is necessary for normal launches between updates. As yours is an initial installation, there may be an operating system XProtect security scan following the click of Open above, and then a secondary dialog will appear with an Open on it. Just click that Open.