Regarding for someone to V phrase

Question

Hello I've got a question regarding for someone to (verb) I'm always curious about "for someone to" phrase.

Here's my examples:

This is first time to see her not tieing up her hair. O
This is first time for her to not tie her hair. X

Why couldn't second one be correct? Or is it gramatically incorrect or grammar is fine but meaning is weird?

As far as I know, "for" can be a subject for "to verb" phrase. For example, "It is fine for me to go there."

I will be really happy if you can let me know if there is a rule.

Answer 1

The question is somewhat unclear, but those sentences would be considered quite awkward. For example, you are using the infinitive of the verb rather than the verb. It would be better phrased:

This is the first time I have seen her not tying up her hair.

This is the first time you have seen her not tying up her hair.

This is the first time she is seen not tying up her hair.

The second sentence would be more clear if written as:

This is the first time she has not tied her hair.

As to the phrase "for someone to", I'm assuming you mean a sentence like

For someone to ride a bike, they must use training wheels.

In this example, to ride is an infinitive, and "to ride a bike" is the infinitive phrase.

Answer 2

This is [the] first time for her to not tie hair”?

This sentence assumes you know the verb to be associated with her. So it's fine as part of a conversation where you would have that knowledge, but not a standalone sentence in text.