To accomplish this task, the user would need to go back to Block2 and compute a brand new Block2 checksum. This exercise by itself would require significant computing power since solving the hashing puzzle is computationally expensive by design. Assuming the user was able to complete this successfully, the malicious user would then need to recalculate a valid checksum for Block3. Remember, Block3's checksum is based on the original Block2's checksum. By changing Block2, Block3, and every block after it are instantly invalid and would need new checksum in order to be considered valid. Every block’s state of validation depends on all the blocks before it. The longer the blockchain gets, the harder it is to change.
The Bitcoin network is a public distributed network, meaning nobody "owns" the blockchain. Nodes in the network work on the principle that the longest valid blockchain wins. As the malicious user starts their attack, it would be impossible to rewrite history and recalculate new valid blocks after the targeted block which was altered. The malicious user would need more computational power than the entire blockchain network. Or, a majority of the current network would need to band together and decide to be evil.
Currently, there is a lot of computing power participating in Bitcoin and other public blockchains. Unless quantum computers become a commodity, blockchains will not be overwritten by a brute force attack like this. There is a very, very small chance that one node could overwrite a couple of blocks at the tip of the chain. However, quickly, nodes that play by the rules would outpace the bad node since they can calculate valid nodes faster than the bad node. Eventually, the correct nodes would produce and agree upon a longer blockchain than what the evil node created, and the network would discard the evil node's blockchain in favor of the correct version.
Want to learn more about how blockchains work? Check out this open-source book called Mastering Bitcoin.