There are a lot of guys who are wearing your same shoes. New relationship, first time sex with her, you want it to be right; this often equals a whole lot of pressure. Pressure causes adrenalin surges and they cause the ED.
My best advice to you is to lay it all out on the line. Confess. Just say to her right up front that the first time you are with a new partner you experience a lot of nervousness and things don’t always work real well. Women love this, actually. They are not accustomed to men admitting that they can be a little fragile and they leap to the challenge - at least the women who are worth their salt do. They do all they can to get you to relax.
A good trick is this: First time together ask her to spend the night. Tell her that your first night together you want to just spend getting to know each other some. Do only relaxing things. Cook together or go somewhere nice. Let her pick a rental movie. Go to bed and snuggle and talk. Rule is, right up front, no sex that night but messing around is OK. If you get hard while you mess around, break your own rule. :) But in the morning you will be rested; your testosterone levels will be higher than at any other time of the day and odds are very high that you will be supercharged. If you are very anxious about all this anyway, take a Cialis the day before.
The next time you are together you won’t need anything because you will have created together a bond of trust with each other having only been in bed together.