She’s adorable! I would describe her as a blue lynx point Domestic Shorthair. She has a wedge-shaped head and large ears, like a Siamese, so I think it’s a possibility that she has some Siamese ancestry.
She's very pretty! I would describe her as a seal lynx point polydactyl domestic shorthair.
Most cats do not have any particular breed ancestry. The recessive gene for colorpoint ("Siamese" point color) originally came from the Siamese breed about 60-70 years ago, but is now widespread in the domestic cat gene pool and doesn't indicate recent Siamese ancestry. It is possible that she has some more recent Siamese ancestry as abyeb mentioned, although this is statistically unlikely, given the small number of Siamese cats out there, compared with the much larger number of domestic shorthairs carrying the colorpoint gene.
As far as Birman ancestry, I don't see any indications of that in your girl. The Birman is a longhaired breed, which is colorpointed like the Siamese but also has white markings on the feet ("gloving"). The Birman is more massive in type than the average domestic cat, with a shorter, broader face. It is also much more rare than the Siamese.