Can you get genital warts if you and your partner never slept with anyone before?

No. It's possible to have genital warts and not know it, not every one gets break outs or symptoms. Your parnter could have had it before meeting you and contracted it with out knowing it.

If you suspect you have it, you should see a doctor and get diagnosed to make sure it's genital warts. If you have done this then have a private chat with your partner and let them know what's been going on.