You can apply for a business credit card even if you haven’t started operating the business yet. You will be liable for any charges on that business credit card and it will be tied to your personal credit and will be reported to the credit bureaus. A business credit card can affect your credit score depending on how responsibly you use it.
If you are not applying several times in a row for a credit card, this won’t hurt your credit score. Your credit score will be affected if you are repeatedly applying for credit cards. If you are applying for a credit card which is only for people with an excellent credit history though, you may get denied and that would be a hard inquiry on your report which will bring your score down by a few points so that is not advisable.