Speaking as an independent breeder....I had to start somewhere, and so I started with Murray McMurray in 1997, 25 Crevecoeurs. They were all definitely Crevecoeurs. I selected my current show stock out of those birds over many generations!
I don't think you can count on getting show-quality stock directly from a hatchery, but it can happen. I had a Missouri State Fair best-of-breed Delaware hen directly from Ideal Hatchery through a local feed store (Fenton Feed Mill, Missouri) around 2008. Mostly, hatcheries deliver the breed you are looking for. I personally have had good luck with Murray McMurray, Ideal, Stromberg, and Cackle Hatcheries.
However, hatcheries will sometimes fill out your order with extra chicks of different breeds they have a surplus of. Murray McMurray used to (and maybe still does) include an extra free chick of an unidentified breed, usually a rooster. In cold weather, extra chicks of a different, unidentified breeds are sometimes added free to your order to keep the entire group of chicks warmer during shipment. This is an inconvenience to a serious breeder, and also to the backyard raiser who has counted out the exact number of chicks their local regulations allow. It's not so bad for someone who can use a few extra birds for the table.
To find independent breeders, I suggest the breeders lists for the various poultry clubs. Search for the breed you are looking for, then add "club" and "poultry" to your search. Many of these clubs sponsor shows, and you can get very good birds from their members.
For more general lists, try the Livestock Conservancy's poultry comparison charts, which compare mostly rare breeds on their conservation list. This is the one for chickens:
https://livestockconservancy.org/index.php/heritage/internal/chicken-chart
Then check their online breeders directory, which includes only members of Livestock Conservancy:
https://livestockconservancy.org/index.php/heritage/internal/breeders-directory
The hatcheries mostly have descriptions of the breeds that they sell, but be aware that some descriptions are more accurate than others.
Another great place to look is feathersite.com's poultry pages, which are an impressive compilation of photos, links, clubs, supplies, housing, for a lot of breeds, including baby chick pictures that can help when you are trying to identify that
TSC chick. Feathersite is a one-person show, so some links are out of date. It's not like backyardchickens.com, no blog-type features, no individual ads.
Another good site is Poultry Show Central. They maintain lists of shows, swap meets, breeder directories and classified ads for poultry, all free. I advertise my birds here. The classified section is a good way to advertise to a mostly poultry keeper audience.
Hope this helps. I left out some, because in my experience the national clubs want you to buy their breeds book, which is expensive but totally worthwhile if you show. I also left out the shows themselves, because we probably won't be having any for a while. When they start up again, attending a show is a great way to learn about and acquire good stock. A lot of the Juniors and 4-H entrants are ready to move on to a new type of bird after the show, and you can get some great birds that have already been shown and handled, and are NPIP-certified.