Is it possible for "thus to" to replace "in order to"

I'm struggling to understand if the sentence below is correct:

The first time they ventured in this bookshop, thus to find refuge and protection from the rain lashing on cobblestones outside, Paul immediately fell in love with the place, as for John, he didn't want to leave it anymore.

Is it possible for "thus to" to replace "in order to"? I'm never sure about the correct usage of "thus"... Also, is it possible to start a sentence with "thus"?

Thank you.

No, it can't necessarily replace it. Sometimes both will fit, but they do not mean the same thing.

Thus can usually be replaced by in this way.

In your example, thus reads oddly, but it is possible. I would read it as a comment from the narrator, "In this way they found refuge", rather than a representation of the characters' intentions.

You certainly can start a sentence with Thus — again, meaning the same as "In this way".

Thus is quite a formal word, not common in speech.

No, that isn't correct. Your sentence would be better without it. (And we normally "venture into" somewhere.) So "...they ventured into this bookshop to find refuge..."

Thus can mean As a result or consequence of this; therefore or in this way. (Lexico) You could say, "I walked into a tree, thus breaking my nose."

Yes, you can start a sentence with it: "I walked into the tree, broke my nose and was taken to hospital. Thus ended my holiday."

(Btw, you need a full stop after "in love with the place.")