My first work authorization in US was the simplest L1b internal company transfer. That took from mid October 2016 to issue of the visa on 21 Feb 2017. That's considerably longer for the simple document.
My blanket work authorization took 2.5 years... and 4 years for the LPR.
7 days for PR in Singapore? That's not the experience I've hear from friends. In fact, you're at the mercy of the gov't as it's entirely discretional for PR. You often have to apply multiple times if you don't have the "right" profile.
An equivalent of what you get in Singapore in 7 days is H1. H1B takes at absolute best - 6 months at 33% success rate.(If you miraculously get to file on March 31st and get to start October 1st.)
Permanent residency in US takes years. Even Diversity Lottery takes at least 18 months.