Live and historical US economic data through the API

Hi. I’m looking to collect and use data such as CPI (inflation report), jobless claims, etc.
I’m looking for the data that’s updated here:

I couldn’t find anything relevant searching through the API docs, would appreciate some help.
I would also like to know if this data gets updated as soon as it’s released - could be very useful for trading bots.

Thank you very much in advance for any assistance!