Was just a conflict perhaps? The Feds saw it more like the Afghanistan conflict, sure it was a nasty little fight and they lost people and the odd ship in nasty circumstances, but it was not the existential battle they face with the Dominion later.
Yes. There were a fair few conflicts in the early-mid 24th century, Cardassians, Tzenkethi, Sheliak, Talarians, however nothing that we know of hit the core systems (specifically Earth) between the Whale Probe of 2286 and the Borg at Wolf 359 in 2367. Post 359 again nothing that the average chef on earth would be concerned with (despite an ongoing war with the Klingons) until a couple of shapeshifters made some noise by bombing the Antwerp Conference in 2372, which killed 27 people (mostly diplomated - a massive event apparently despite 27 people being killed every day on normal starfleet away teams), and the establishment decided to use that to grab power. Amazing what 4 people and a lot of fear can cause.
DS9 in the mid-late 90s was a good foreshadowing of the US a decade later.
A few years later of course and the Breen managed to shock Earth some more with an attack on the Golden Gate bridge, and Betazed was sacrificed (a whole fleet on a "training exercise" in the middle of a war?) to ensure continuing support for the war. Galactic Politics, and the view from home, by this point had moved on a long way since the idealised days of the 2360s, where the Federation's battles were out of site, out of mind, and information on them could be tightly controlled.
The parallels between the dominion war, which moved from a cold war with isolated scuffles into a hot war with millions dead, and the Klingons, which moved from a cold war with isolated scuffles to avoiding a hot war thanks to Kirk and co in 2293 is striking.