I will share it with you for your reference.
I use 1 password to login to the management console. 
 Password management tool for families, businesses, and teams | 1Password
With 1 password, you can enter your Account ID, username, password, etc. with 1 click.
However, please note that there is a fee for 1 password.
There is another way to log in using scraping, which I found in an article in Japanese. 
 Automating AWS Console Login with Python selenium (Scraping Web Screens with Python) - Qiita
I hope this is helpful.
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