Which country are you in? There are multiple different country-specific Amazon sites.
edit: The links are:
The Expanse is not available in Cuba, Iran, Mainland China, North Korea, and Syria, but one of the links above should work for all other regions and all 3 seasons should be included.
Make sure any VPN is disabled.
edit: Added Japan link. It couldn't be found by Amazon search with the English name.
Amazon will stream it internationally simultaneously. They've also just added the first two seasons in Ultra HD 4K to the US service, which is great.
https://www.amazon.com/Expanse-Season-Ultra-HD/dp/B01MT0UHLT
The question will be what happens to Season 3. That depends if Amazon buy out Netflix's deal and move the first two seasons to Amazon Prime and can then show Season 3 immediately, or if they simply take over the deal, so Seasons 1-2 will remain on Netflix, Season 3 will air in the autumn and then Season 4 will be on Amazon. Those details haven't been announced yet.