Travel by High Speed Train From Hong-Kong to Shenzhen

I am a Dutch citizen traveling with my family (all Dutch citizens) and plan to travel from Hong Kong (West Kowloon) to Shenzhen via high-speed train. We intend to stay for a maximum of 4 days.

Are we eligible for the 5-day Visa on Arrival (VOA) or the 144-hour visa-free transit? Most resources I’ve found focus on air travel, with little information about high-speed train travel.

Is there a daily limit on the number of visas issued? Some sources suggest travelers have been turned away due to a lack of available visas at the designated stations. Could you clarify this?