Umm no they had not... I don't now where you got that bit of fantasy from.
Circa 1865/66 was just about when most Europeans were also just implementing their first Breech loading conversion weapons - not bolt action. The US was at no disadvantage here.
France: while it may have adopted the Chassepot in 1866 it was still also converting its muzzle loaders under the Tabatière rifle system. Even by the Franco Prussian war the conversions still made up a fair amount of French guns on hand.
UK: Used the Snider-Enfield conversion until the 1871 and the introduction of Martini Henry
Austria looks to have used the muzzle loading Lorenzs as late as 1866 when the standard muzzle Loading was the main long arm. The Wanzl conversion does not appear to have been adopted before the 1866 lost to Prussia. The M1867 Werndl-Holub replaced in the next year or so (slowly).
Yes Prussia does singularly (OK and Norway) emerge as a switching in to a single shot breech loader in the Dreyse 'needle gun' circa mid 1840- but one with a lot of issues and problems (see below - new post I did not mean post this yet so more later). Also I cannot find a good source but like much of Europe Prussia seems to have retained lancers and a pile load of silly cavalry traditions just not quite as bad as everyone else so balance that enthusiasm so let's not get too sloppy about how great they were..
It took long enough to track down the Austrian guns so I'm not going to do it for Russia or anyone else, but broadly speaking in Europe 1866 or so was when most powers moved to at minimum to a breech loading conversion for front line troops out of the old solid muzzle loading standing stockpile. Nobody went bat crap crazy and in general not until the mid 1870 could you have expected every major power to have a modern breach loader in the hands of its front line troops that includes Prussia dealing with all the down sides of the original needle gun.
So in fact the US was in fact with or ahead of the times by 1865. By 1866 the US was on it second round of implementing the
Allin designed trapdoor breech-loading mechanism conversion of the Springfield Model 1863 the first being started in 1865. At the same time time US had free access to what was clearly the best breach (clip loaded/magazine) loading firearm of the day in in The Spencer Repeater carbine or rifle - that sorry to say cleans the floor with the Dreyse. Not only that the US had the Peabody breach loading system available as early as 1863/4. If the US wanted to or had fought Europe in 1865 it had more or less the best small arms tech on hand to use.