Checking your eligibility will not affect your credit score. We use what's called a "soft pull" — as opposed to a hard pull — to determine your eligibility and get you the best offer possible. Soft pulls do not affect credit scores.
However, if you're approved for a loan and sign a contract, there is a hard pull that may temporarily affect your credit score. This hard pull only happens after the contract is signed, and you can build credit history by making on-time payments.