Is it possible to crash or shut down the entire Internet?
No. The Internet as a whole is a collection of many independent networks controlled and maintained by different people, businesses, and governments. It's designed to be redundant. Which means even if one portion of the network goes down, users should still be able to access all or some of the other available networks.
It's still possible for the Internet to experience outages often caused by severe events such as large power outages and earthquakes. When large outages occur, a sizeable portion of the Internet or even an entire country may be affected. However, even these serious outages will not cause the Internet to shut down or crash. For example, in early 2007, Asia experienced several earthquakes that damaged undersea cables that caused wide Internet and phone-related issues in that part of the world. However, the remainder of the world still had access to the Internet.
Internet blocked by countries
Some governments can set up firewalls and other protection schemes to prevent users from accessing pages on the Internet or block access to the Internet. For example, in 2011, the Egyptian government shut down the Internet several times during protests to prevent any information leaking out onto the Internet. However, even during this strict shutdown, citizens were still able to find ways to access the Internet.
Network configuration problems
Although there are measures to help protect the network equipment that helps run the Internet, it's still possible for the humans controlling that equipment to make mistakes. Improperly configuring or updating equipment can cause outages to portions of the Internet. For example, in 2019, Verizon caused a BGP (Border Gateway Protocol) route leak that caused problems for many services, including Cloudflare and AWS. Because many websites and services rely on these companies, it caused hundreds of websites and services to be unavailable for almost two hours. However, many sites and services not reliant on these services continued to work.
Attacks like a DDoS attack can cause many problems for a website or service. These attacks are designed to overwhelm a company with so many requests that it stops working. These types of attacks can disable one or a few websites for a short period. However, the attacks only disable a website or service running on the Internet and not the Internet as a whole.