Is there a way or api to register Url on Google? For example, when a page was created in the project, its address will be automatically submit to Googlebot.
There isn't really a way to submit it automatically (otherwise there would be no captcha).
However why do you want to submit every page to GoogleBot? It is sufficient to point the bot to your project's address once the project goes online (if Google didn't already found your project). GoogleBot is regularly visiting your project, automatically adding/removing new and old pages in your project (as soon as there is somewhere in your project a link pointing to the new page).