In terms of access, breech-loaders were available to civilians from the beginning. In fact, prior to their mid-19th century adoption by the European national armies, the development of breech loading firearms were primarily sponsored by civilian needs. Specifically, for sporting, i.e. hunting.
Experiments into the development of breech-loaders continued for the following century and a half but were principally aimed at the civilian market for sporting firearms; not until the early 18th century did a breech-loading system suitable not only for large-scale production but also for handling by soldiers attract attention of military authorities.
- Holmes, R., ed. 2001. The Oxford Companion to Military History. Oxford: Oxford University Press.
While available, the principal barrier against civilian (and government) adoption of breech-loaders is their cost of production. This was a factor as late as the American Civil War, when qualitatively superior breech-loaders were still outnumbered by cheaper, more easily produced muzzleloaders.
At the same time however the Industrial Revolution was rapidly enabling factories to mass produce these rifles. In Europe, it took Johann Nicolaus von Dreyse's factory from 1841 to 1863 to equip the Prussian Army with 300,000 of his famous needle gun. Yet by 1866, the French were churning out 300,000 chasseopt rifles a year in Puteaux.
[Dreyse's factory] had taken more than two decades to equip the troops with the needle-gun.
- Förster, Stig, and Jorg Nagler. On the Road to Total War: The American Civil War and the German Wars of Unification, 1861-1871. Cambridge University Press, 2002.
[I]n 1866 the French government re-equipped the armoury at Puteaux with 'interchangeable parts' machinery capable of producing 300,000 of the new Chassepot rifles each year.
- Keegan, John. The Second World War. Random House, 2011.
Though these were military production, the innovations in machine tooling and production methods occurred in lockstep with private industry. Furthermore, many surplus or captures military weapons were repurposed for sale to civilian markets in this period. By the end of the 1800s, the Boer farmers of South Africa were going head to head with the British Empire equipped with breechloaders.
Nonetheless, the relatively lower cost and convenience of both gun and ammunition for muzzleloaders allowed it to preserver in some capacity. Not to mention its popularity today in the form of replicas.
As a matter of fact, single and double-barrel muzzleloading percussion shotguns were still popular until the early twentieth century. This wasn't due to reluctance by hunters to accept the new breechloaders, but rather, because the muzzleloaders were cheaper and didn't require expensive shotgun shells. For a largely rural population, it was simple economics.
- Barnes, Frank C. Cartridges of the World. Gun Digest Books, 2009.