Putting "to + verb" at the beginning?

Hello my friends.While studying at adverbial and adjectival functions(phrases/clauses), I saw a suggestion to understand what is an adjectival or adverbial. The suggestion is to put them at the beginning and figure out whether they work or notor instead of this, we can ask some questions to the main verb of sentence.If they work and answer, it means they can function as an adverbial.If they don't, they can not.On this way even if native English speakers don't prefer, putting them at the beginning is grammatically/ technically correct or not?

Examples,
1-) I need some time to think about my problems.
Can we have place "to think" at the beginning? I think yes we can because we can ask a question like"What do you need some time to do?"
It means it can function as an adverbial.So "To think about my problems, I need some time." makes sense and there is no grammatical problem.

2-) I have no reason to buy a new car.
The same question as example 1. Can we have place "to buy a new car" at the beginning?
I think yes we can, again. Because this question makes sense, "What don't have a reason to do/in order to do?"

My final conclusion is that we can put these kinds of sentences at the beginning
(even if there is no need to put them at the beginning and no one prefers, I am just asking to learn)
and they make sense without any grammatical(also meaning) problems.

Do you agree with me?
Thank you very much.