Kairos is in a pretty early stage. They started building a test reactor this summer, scheduled for completion by 2027:
https://www.energy.gov/ne/articles/kairos-power-starts-const...
EDIT: Statement from the official Google announcement linked by xnx below [2]:
Today, we’re building on these efforts by signing the world’s first corporate agreement to purchase nuclear energy from multiple small modular reactors (SMRs) to be developed by Kairos Power. The initial phase of work is intended to bring Kairos Power’s first SMR online quickly and safely by 2030, followed by additional reactor deployments through 2035. Overall, this deal will enable up to 500 MW of new 24/7 carbon-free power to U.S. electricity grids and help more communities benefit from clean and affordable nuclear power.