You can do this with Conditional Contact Form 7 plugin, for each values in your first dropdown you need to create a corresponding dropdown field,
`[select first-dropdown “chose a value” “value 1” “value 2”]
[group dropdown-value-1]
[select value-1-dropdown “chose option for value 1” “value 1a” “value 1b”]
[/group]
[group dropdown-value-2]
[select value-2-dropdown “chose option for value 2” “value 2a” “value 2b”]
[/group]
dropdown-value-1` group when ‘value 1’ is selected in the first dropdpwn and so on. See this tutorial which explains all the steps in details.
You then need to setup your visibility rules, and to show