I had to have 3,000 TT and 1,000 MEL before I could get my first King Air job. After the 1,000 piston MEL (night freight) it was relatively easy to progress into turbro-props and multiple corporate jets.
When I got hired at an airline, I had 12 years of part 91 and 135 work, 5 corporate jet type ratings and 7,000 TT - around 3,000 Jet PIC. Seemed reasonable at the time. I guess, in full disclosure, I was hired to be a Captain within 3 to 5 months - and was.
I think the ATP and at least 500 multi is not too much to ask.