Israel was one of the first to vaccinate most of their population - and they are a tiny country with no domestic manufacturing of the vaccines.
Although Israel quite openly stated they paid a premium to get early access to vaccines. So basically, it was simply a question of commercials, and ponying up the cahs.
Singapore did likewise - basically bought out every vaccine they could on the open market, and rushed to vaccinate their population.
I live in Australia, and it does appear our nation's leaders dragged their feet on the vaccine.
Our Prime Minister even publicly stated "It's not a race", regarding vaccinating the population.
A letter leaked recently, which showed Pfizer's managing director requesting an urgent meeting with our health minister, so we could get millions of doses. Pfizer was then told that the health minister wasn't available to talk with them, it got fobbed to some underlying in his department, then the deal got adragged out for six months after that - in the meantime, the UK and US signed up:
https://www.theguardian.com/australia-news/2021/sep/12/in-hi...