Importing private key to bitcoin node is slow. Can it be faster? I have launched the bitcoin node and synchronized it. The issue is that importing the private key forces the node to scan the blockchain for the operations with the key. Is there a way to import the key in a fast way?
No.

Bitcoin core is a full node and doesn't use SPV or any equivalent. Therefore, when importing a private key, it must scan the Blockchain copy it holds rather than trust third parties.

Sweeping the private key into Bitcoin core ought to be faster.