SQLite Forum

Insert operation leads to exception on Windows when installed using msi
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You need to arrange that, once installed, your application can be used by those for whom it is intended to be used. This means that the DB file will need to have permissions consistent with modification by those users.

How to achieve that using your preferred installer software is off-topic here. Whether the solution is to use installer features or some kind of post-install fixup script, discussion of it should happen elsewhere. I expect there are fora dedicated to your installer where your problem would be readily solved and topical.

You might also consider having the application itself create the DB file when it does not yet exist.