Can the Nonce Be Used to Reverse-Engineer the Block’s Data?

No, the nonce cannot be used to reverse-engineer the block's data. The hash function is a one-way function, meaning that while you can easily verify the output (the block hash) given the input (the block data including the nonce), you cannot derive the input from the output.

The nonce is merely one piece of the input that satisfied the difficulty target.

How Is a Second-Preimage Attack Different from a First-Preimage Attack?
How Does the Size of the Hash Output (E.g. SHA-256) Relate to the Nonce?
Define ‘Cryptographic Hash Function’ and Its Key Properties
What Is the Difference between Hashing and Encryption?
Is a Similar One-Way Function Used to Calculate the Price of an Options Derivative?
How Would the Inability to Reverse the Function Break Cryptocurrency Security?
What Makes the ECDSA Process “One-Way” and Why Is This Critical for Security?
How Does a Hash Function Differ from an Encryption Algorithm?

Glossar