to vs to have

The key to a high speaking score isn’t your use of ‘complex’ grammar structures, big words or idiomatic phrases. The key is to speak as naturally as possible, and real examples or stories help you to do this.

How about if I use “to have” instead of “to” in the sentence above?

That wouldn’t work. In this sense “the key to…” needs to be followed by a noun or noun phrase. You could say “The key to having a high speaking score…”, though I think I prefer the original.

Can I replace “to” by “belong to” in the sentence? Or could you suggest some alternates for this?

Do you mean “The key belong to a high speaking score…”?

That doesn’t make sense.

There is no reason to want to change the original. “the key to …” is more or less a set form of words.

This usage of “to” is new to me and I am trying to understand it. In this case, I think it is used as a preposition but can’t find it in Longman English Dictionary. Here is a list about its usage as a preposition:

It is used as in definition 4 in this link:

  1. —used as a function word to indicate addition, attachment, connection, belonging, possession, accompaniment, or response

“a high speaking score” is attached or connected to “the key”