You need to pay more attention to the first word in your quotation IF....
Yeah. And considering he was talking about launching a full scale invasion of the western territories by expanding his anti-French animosities to Spain, and perhaps even turning southward to Mexico and South America, that's a pretty damn big IF.
Those letters reveal the unguarded Hamilton speaking to his confidants about his political dream, and that dream entailed provoking a war of continent-wide conquest. How else do you explain Hamilton's outright loathing and furious reaction when Adams appointed Murray as special envoy to France and successfully negotiated a peaceful end to the Quasi War? No sane man could fault Adams for that - only a madman who enjoyed the war and wished for its escalation. And those letters reveal that Hamilton was such a man.
Fortunately your hallucinations have no bearing.
Our army was not even capable defeating Indian tribes much less invade the Southwest. Nor would the increase in military force allow such an endeavor.
I have already explained the opposition to Adams negotiations with France. He objected to crawling back to France and saying “thank you, sir may I have another.” It had already been tried and the nation was furious at the humiliation our envoys were subjected to.
Hamilton was unwavering in the policy of Neutrality which infuriated the democrats.