Yes, it is possible. I was diagnosed with genital type 1 5 months ago after a 1.5 year relation ship where my bf has absolutely NO symtoms any where (face or genital) and I'm still like, what the hell? where did this come from? But there's some thing I'm sure of and that is I've gotten it through oral sex performed on me.
It could be either my bf has it orally with NO symptoms and just gave it to me after 1.5 years or I've had it hidden and showed up 5 months ago, it's a f...ing weired virus.
I don't think I can ever know how or when I got this.