Make a script that will be registered on the site

Hello! Straight to the task:
We are now developing a certain service, we need a script that will be registered on the site - https://new.faberlic.com/ru/register for those data that the user fills in on our page, in response the script returns a link for authorization (I will show an example), as well as an ID in the system (it is registered in the header of the profile, there is a redirect after registration). No confirmations are required, that is, the task is simply to fill out the form on that page of the site and send it.
You cant write a script on your own.

What is known:
- No official API
- On the google recapcha page
- The site has javascript cookies, their verification occurs when sending the form
- There is an IP block

I couldnt write a PHP script.

What you need from you:
Write a script that will accept data (POST or GET request in any format), register, and return data (even with text separated by commas, it does not matter). You also need to provide for the possibility of using a proxy. No further action is required.

Estimated budget - 5.000
By timing - the sooner the better
What language will you write in? Any suggestions?