counting layers is not how age is calculated
I think that assumption is well represented in literature.
AntarticGlaciers.org says:
Layers In The Ice
If we want to reconstruct past air temperatures, one of the most critical parameters is the age of the ice being analysed. Fortunately, ice cores preserve annual layers, making it simple to date the ice. Seasonal differences in the snow properties create layers – just like rings in trees. Unfortunately, annual layers become harder to see deeper in the ice core. Other ways of dating ice cores include geochemisty, layers of ash (tephra), electrical conductivity, and using numerical flow models to understand age-depth relationships.
This 19 cm long of GISP2 ice core from 1855 m depth shows annual layers in the ice. This section contains 11 annual layers with summer layers (arrowed) sandwiched between darker winter layers. From the US National Oceanic and Atmospheric Administration, Wikimedia Commons.