https://www.upstreamonline.com/field-development/foreign-led-oper...

https://www.upstreamonline.com/field-development/foreign-led-operator-starts-kazakh-field-facility-to-deliver-light-oil-to-european-buyers/2-1-1673341

Interesting part:
"Karachaganak liquids are shipped to European and US markets via a dedicated oil export pipeline from Kazakhstan to a Black Sea terminal in Russia that is operated by Caspian Pipeline Consortium"

Looks like there are ways to export out, just need to get large enough BOPD to facilitate agreements with international companies. Not sure about the costs associated with it however. Given Kazakhstan has exceeded oil production a few times for OPEC, they might struggle to find extra quota that hasn't already been granted for exports.