For example, I really like the designs of Google pages. Google offers Material.io with which you can design this really similar. Is it allowed to design your own website very similar to another?
You cannot copy or imitate assets that fall under copyright protection, and you must not cause confusion with competitor's websites. So for example you can't copy Google's CSS files or SVG icons, and you cannot imitate their site design so closely that a reasonable visitor would think that your site was a Google site.
Furthermore, the appearance/design of elements of a user interface could be protected via design patents (industrial design rights). Google has various design patents relating to material design, e.g. screen layouts, icons, animations, or some components. E.g. USD802004 is a design patent on the animation of a screen used in Google Maps.
But aside from that, you are free to imitate the design of a website.
Material.io and the Material Components libraries are a special case: Google has developed a design language and offers components that implement this design language under the MIT license, an open source license. This confirms your right to use these components without restriction, without payment, and for whatever purpose you want. Thus, creating a website with Material components is perfectly fine. Using the Material design language without these components could perhaps be fine because Material Design is not protected itself, but you'd have to tread carefully.