Is it normal for your first period after you lose your virginity to be different than usual?

The only reason there would be blood from sex, is from your hymen breaking. That's on the outside of your vagina, so would be visible immediately after intercourse, & when you wiped after sex, as a fresh, red bleed. It wouldn't cause blood higher up in your vagina, or affect your periods.

I cannot think of any reason why intercourse would make your next period different. Only, perhaps, if you had contracted a sexually transmitted disease, & an infection was present & affecting you internally (I'm thinking discoloured or bloody mucus, for example).
It's possible to carry a sexually transmitted disease without symptoms, for some time, with some STDs, & some, even by a virgin. If you were both tested before having sex for the first time, though, then that would be unlikely.

Sometimes intercourse can make blood that's almost ready to come away from the uterus/cervix, come away sooner/more quickly, but that is usually in the few hours after sex.

Are you sure that this is a period? Is there any chance you could be pregnant? That could give you implantation bleeding, which can be a mixture of brown, or pink, or red blood. It's also possible to have what you think are period during pregnancy.
If not, then, as you say, brown blood can come commonly at the start or end of a period. It may just be one of those things. I get that, often.