Yeah wait for revisions. There’s been some multi-sigma shenanigans at first print in the recent past
You make a good point about these types of numbers. It's hard to get accurate and timely data in the field of economics, and headlines will never show the revisions, so the information we see will usually be the least accurate (assuming accuracy grows with time).
That said, these are good numbers and there's no reason to suspect they're not real.
Also accounting for multiple part time jobs vs a full time job
For those who're wondering what the sigma beat was this time, it was a 4-sigma beat, which is pretty large.