Is there an accurate way to date conception?

Patient: My lover is pregnant. Her LMP was June 4th. She has had her 2nd ultrasound today. The EDD is 11th March, but based on the LMP. Her cycle has always been a little irregular (completely in fact until the April, May and June). We had sex but used a withdrawal method, although I did ejaculate on the surface of her vagina, on 27th June. Please don’t judge, but she is married and had unprotected sex around 18th June – which fits the ‘standard’ ovulation date. What chance – I realise it may not have a % but ‘approximately’ – is it that the baby was conceived in 27th June, given the ‘withdrawal’ method and the distance from the ‘standard’. I do want this to be my baby as does she, but we both feel it isn’t. The nurse at the 2nd ultrasound (today) said that the embryo was larger than ‘expected’ and growing well – I’m not sure if that lends itself to an earlier conception date or not, or, as I am western and she (and her husband) are Asian, this might make it more likely to be mine. I know no-one can ‘guarantee’ either way without testing but I have read some forums/used some calculators that seem to show it’s an minutely small chance of being mine, but others have said you can conceive at any point…

Symptoms: pregnancy