First time jitters happen whether you are having sex for the first time or having sex with a new person for the first time. It is normal.
When having sex with a new partner, it is normal to feel that you want to impress them. A lot of effort goes into meeting someone, getting a first date, having a date, and keeping them interested enough to want to have sex. It would be a let down after all that effort to have the sex be not so good. Also, if the sex is not good, that increases the chance that the woman won't want more sex in the future. If the woman doesn't want more sex from you in the future, you're back at Step One. For guys who want more than one night stands, that's a bummer.