If a girl has just started birthcontrol and she has sex with her boyfriend and he cums inside of her can she get pregnant?

And if she is pregnant how soon will the symptoms come ?

No birth control is 100%. If semen is ejaculated into the vagina, there is always a risk of pregnancy. Depending on where in the cycle the woman is, symptoms can take a few weeks to show.

I'll say it again, NO ONE should engage in sexual intercourse unless they are financially and emotionally ready to have a child.

As ScottGem said, birth control pills are not 100% effective. Taken as directed, they offer very good protection, but pregnancies do sometimes occur. Generally it is recommended to wait at least a week, a few weeks would be even better, before relying just on the pill. It is usually suggested to use an additional form of birth control, such as a condom, until that time.
If pregnancy occurs, some women will notice symptoms within the first couple of weeks, even before a missed period... but most will find it takes several weeks for more obvious signs.
Think very carefully about continuing to engage in sex if you and your partner are not in a position to care properly for a child as that is always a possibility. Everyone thinks it won't happen to them, but it can, and you could very well be the person it happens to. DO NOT allow anyone to talk you into taking any chances if you are not comfortable. You are the one who would have to go through a pregnancy, You are the one who would have to give up the most, You are the one who would be ultimately responsible for a child, You need to protect yourself.