Daughter: But, in that case tanzaku are meaningless aren't they?
Dad: It's okay
Daughter: What! Because you say it's okay?
I understand すぐ to mean soon/immediately etc. I can't understand what it means in this context.
My guess it that it adds the meaning 'just' as in "am I supposed to believe it's okay just because you say so?". But that's a complete guess and the link with 'soon'/'immediately' seems very tenuous.
If further context is needed, these lines follow immediately after this question: