Only a very small amount of martensite is formed in metastable austenitic stainless steels by cooling to cryogenic temperatures. In the article

Lee, Jae-hwa, Takashi Fukuda, and Tomoyuki Kakeshita. "Time-Temperature-Transformation Diagram of Successive γ→ ε′→ α′ Martensitic Transformation in SUS304L Stainless Steel." Materials transactions (2008)

the authors held SUS304L for 7000 seconds at -100K and produced only 0.5% of martensite.

A higher amount of martensite can be produced by stress-induced or strain-induced martensitic transformation. In this case, You assist the martensitic transformation through external stress. If the stress is below the yield stress, we talk about stress-induced transformation. And if the stress is higher than the yield strength, i.e., enough to produce plastic deformations, we talk about strain-induced plastic transformation.

Sometimes You can produce strain-induced martensite on the metallographic specimens just by polishing them. The stability of austenite with respect to strain-induced martensitic transformation is usually characterized in terms of the MD30 temperature calculated using the Nohara equation. High MD30 temperature = unstable material.