You are talking about the December that just went by, is that correct? (In other words, as of now she is in her 10th week or so?) How early were the "early scans?"
I am a little surprised she would be "adamant" that the baby is not from the sex with you. The fact that she insists (instead of leaving the question more open) suggests that either she doesn't know what a doctor means when he says "You are 10 weeks pregnant," and thinks it means that is when she conceived, or that she really, really, really wants the baby to be from her boyfriend to the point that her mind rejects all other possibilities. (This might be a fair thing to think, if you used protection. Did you?)
I guess there are some more far-fetched possibilities, such as if she had her IUD removed a few days after sex with you, or used some esoteric method of female birth control with you that had worn off by a few days later. Did she take the morning-after pill after the sex with you?
Anyway, I think most women who are pregnant and aren't sure who the dad is will let fairness rule and will at least give the guy a chance to get a DNA test. Keep the lines of communication open with her and look for an opportunity to discuss this again.
Do you have the exact date of her first scan that provided the due date of August 30?
You need to speak to attorney in the state that the woman who is potentially carrying your child lives in immediately.
Let's say it is your child. And she raises it with the boyfriend. And they break up. And she can't afford to take care of the kid by herself. Lets say the kid is 8 years old and you've never met. She can file against you for child support. You will be forced to submit to a paternity test, and if it is positive you will owe her approximately 35% of your income until the child is 18. Plus day care, plus medical expenses. In fact, depending on the state you may be found liable backdated to the day of the child's birth. You will be giving someone all of your money for a child you have no relationship with. If she wants to she can pick up and move to china with the kid and theres nothing you can do about it, but you still have to pay.
How to avoid it?
File a paternity suit against her as soon as the child is born asking for full or partial custody. She will be forced to DNA test the child. If its yours, its likely you may get 50% or more, they don't really favor the mother anymore for custody as long as you have been significantly involved in the child's life from the beginning. If you win youll owe her very little, or she will owe you. If you lose, well then you're in the same situation as you would be above, but you still get visitation rights (yes she will be forced to send the kid to you for the summer from china if you want it) and at least you have a relationship with the kid you are paying for. You're paying for something that benefits you and not for a kid somewhere you've never met and who believes someone else is daddy.
How well do you know this woman? Do you trust her? I just want to you to be aware of what she can legally do to you if you are wrong. Do not stick your head under the rug about this, even if she will not admit right now that it may be your child. She can change her mind at any time if it is yours and you are responsible for it.
So I think you mentioned earlier she lives in California- Lets say hypothetically she doesn't work at all, and you earn 40k a year. If this was the case your child support payment would about $726 a month. Im not sure about CA, but in my state you have to pay 50% of any healthcare and 50% of childcare costs on top of that. And, it can actually be even worse than that.
Lets say she really really hates you and lets say she has a good lawyer. They can also do something called imputing income, which means they can hold you liable for money you don't actually earn. Lets say you used to earn 50K, but a few months ago you either quit your job or got fired for whatever reason. You have a new job now, and maybe you're much happier than you were with the old job but this job only pays 35K. If it can be argued that you voluntarily switched to the lower paying job, they can still use 50k to calculate what you owe even though now you earn much less. Imputed income can get pretty scary.
I know someone who picked up a ton of overtime after he broke up with his gf, he was depressed and didnt want alone time and his job had a project he volunteered for where he started putting in 80 hours a week and was making a ton of money (40 hours plus 40 hours of time and half) Then he found out they can consider his 80 hour a week pay his normal pay, which means his childsupport payment would actually have exceeded his normal 40 hour a week paycheck and he could be forced to continue working 80 hours a week until the kid turns 18. (Or go to jail for failure to pay child support) Luckily his ex wasn't out for blood, but the legislation is pretty tough on people who actually work for a living due to efforts to crack down on deadbeat dads back in the 80's and 90's.
There are some states where something like 20% of their prison populations are made up of people who won't (or most likely can't) make their child support payments.
Also, you should know that even if the girl does not want child support money from you, there are other ways you can get hammered by this. Another friend of , just got hit with a support order out of another state (GA) for a girl he didn't even know he knocked up on a one night stand when he visited atlanta 5 years ago. This girl did not take him to court, she didn't want any money from him. She never told him he was the dad and decided to raise the child on her own.
But at some point later she had to apply for welfare. The government made her name the suspected father of the child in order to collect benefits and then the department of revenue tracked him down, dna tested him, and forced him to payback the benefits she got from the government plus child support. He earns $20 per hour working retail and his payment is $900 a month now for a kid hat lives 500 miles away whom hes never met and didn't even know existed. Its really no joke.
I'm just giving you worst case scenarios, not saying any of this will happen to you. But please talk to an attorney about your options if she will not agree to be reasonable and allow you to make sure its not your kid.