Hydrogen formation during wet processes, including pre-processes, occurs in the following scenario.
During pickling, following chemical reaction occurs.

As seen above, hydrogen does not form when oxides only dissolve, but hydrogen ion is generated if the base steel alloy is dissolved also.
In zinc plating, redox of the zinc and electrolysis of water causes hydrogen ions, and hydrogen is formed.

Hydrogen ions generated as seen above immediately becomes atomic state hydrogen H, and the hydrogen penetrates the steel alloy's interstitial structure.

In this scenario, hydrogen will not be formed if all the electrical energy applied is spent on zinc metal deposition (redox). This condition is called Cathode Current Efficiency = 100%.
This cathode current efficiency varies depending on plating bath composition and cathode current density, etc. In general, the cathode current efficiency is good with mildly acidic single salt bath for nickel plating bath, but the efficiency tends to be low in zinc cyanide plating bath, and the hydrogen formation increases as the current density becomes higher.

Additionally, hydrogen overvoltage is another dominating factor for the formation of hydrogen during plating. Hydrogen overvoltage is an electrical potential difference that exists between atomic state hydrogen (H) becoming gaseous state hydrogen (H2) when the hydrogen ions electrically discharge on the surface of the host metal, and it varies with metal surface conditions. Generally, it is high for metals with low melting point, and small when the surfaces are rough. Hydrogen is more easily formed when hydrogen overvoltage is small.

Therefore, more hydrogen is generated during precious metal plating such as gold and silver, but less for zinc and tin plating. For instance, when zinc plating steel alloys, initial hydrogen generation is small since the hydrogen overvoltage is small with the steel alloy, but once the base metal is covered with zinc the hydrogen overvoltage increases thus the hydrogen generation is reduced.

The hydrogen generated here will penetrate the host metal as atomic state hydrogen. It is generally said that gaseous hydrogen cannot penetrate the host metal. Therefore, it can be assumed that hydrogen embrittlement will not occur if all the generated hydrogen is gasified and dispersed. A plating bath with chemical additives that promote such a reaction is highly anticipated.