You're not supposed to "believe" anything. You can learn physics from zero and follow the full reasoning to the several competing theories that try to explain the functioning of the universe. What you're supposed to do with them is question them, test them and try to invalidate them and come up with a more precise theory. The exact opposite of what you're saying. Don't trust, verify.
Discussion
Forgot to add - I also reject completely your claim that science leads to nihilism. If anything, it looks like people who feel a need for some mysterious, supernatural (?) "purpose" are easy prey for nihilism. That's why such people must have unquestioned belief in unproven and unprovable things. I'm perfectly fine with questions and enjoying the most probable explanation: that there is no "purpose" to the universe, that the universe simply is, and that How does it work?" is a valid, productive question that leads to our betterment, unlike "To what purpose?", which only leads to unprovable, unproductive false answers.
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