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Suggestion: Use strong hashes on the download page
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> I explained my situation, which is that Windows out-of-the-box does not provide a tool to verify the provided sha3sum. There are numerous possible workarounds, none of them are ideal.

Here is yet another suggestion:

Since security is important to your company, and in particular
security associated with SQLite databases and the programs used to access
those databases, perhaps your
company could enter into a [paid technical support][1] arrangement
with the SQLite developers.  In that way, you would help to fund our
continuous and ongoing efforts to protect the SQLite code base from
unauthorized tampering.  And as a paying client, you can probably convince us
to send full-vetted SQLite source files or builds to you via whatever
secure channel you find most convenient.

[1]: https://www.sqlite.org/prosupport.html

By returning a very small percentage of the value you receive from
SQLite back to the SQLite developers (still keeping the vast
majority of that value for yourselves), you will be helping to protect
your supply chain and at the same time simplifying your own operations
by making it easier to obtain validated and trusted SQLite code.