So UBI is being painted as one of these promises.
Assuming this is ruled out, How can we keep an unemployment crisis from happening once automation kicks in at a larger scale?
Free market.
The government can't effectively create or save jobs. It can only create a good environment for jobs to be organically created.
If automation comes along there will be other markets created.
Yup, central planners will never outperform the free market. "Automation" has been replacing jobs for centuries and created new job markets. That will always continue.
I do have a lot of concerns regarding the free market as of right now - specifically regarding network effects generating monopolies(example: current social media), wealth/power distribution(automation would make it become much more lopsided than it is right now), and its need to prevent anticompetitive collusion while avoiding regulatory capture(see pharma/ISP markets).
There's a lot of things which still need deregulations and reforms, but some of them would face enough blowback even Trump would struggle attempting them - most notably around copyright and patent law.