When you go to www.axieinfinity.com, trust me you will never find a link that will let you register an account.
You may try going to https://marketplace.axieinfinity.com/, that page looks promising because it has a Login link on the upper right corner.
To make it simpler, just go straight to this link, https://marketplace.axieinfinity.com/login.
It will take you to this page.
I told you, still no link for registering an account.
But, the page looks promising. It has three (3) buttons to choose from, so that you can login to Axie Infinity.