Reaching out to managers at big cos won't get you much. They are getting a ton of twitter/etc candidates and have stricter hiring policies and rubrics to prevent nepotism and favoritism. If you can network and ask for referrals through your friends / professors that can work better. Or reaching out to early stage startup cofounders can work really well.
ML/AI is less frozen then some other areas so that is good. Most really competitive new PHDs will have either a couple of internships, strong academic contributions or previous engineering experience demonstrating strong coding ability.
You should also consider post docs or academic engineer postings. The grant cycle insulates these a bit from the economic cycle and they can be a good place to gather some experience while you ride out the cycle.
And definitely consider very early stage start ups. A startup that just raised and has 2 years of runway is probably one of the safest places to be at the moment as they are still focused on growth. A lot of great companies proved themselves as startups during the 2008 cycle and grew rapidly after. Networking can mean a lot more here as early stage founders often literally just hire their friends or people they get along with without a ton of process.