No. When you find this truth, you may want to tell others about it. Then you will promote this truth.

is promote suitable words to express the search for truth in scientific writing context?

Promote is to make something become more advanced or encourage the progress of something. But promote does not mean search. You can only use promote to say that you are advancing the search so that more people know about it.

nope. What's the question, exactly? I can promote a search for truth. I can promote the idea of knowing the truth, which may lead some people to searching for it. I can promote others to give better answers, which might make finding the truth easier.