"Your odds at 40 of a baby are around 50% and at 37 around 75% "
It's 40-50% and then the miscarriage rate is higher, by 43 it drops down to 1/2%. The Women who are managing to do it without IVF must all be known to a MN'er, if you believe the posts.
OP, if you actively look then it could be possible, but having a baby with someone you've known so little time, doesn't guarantee that the relationship will last, so chose someone that you think will support the child.
Personally, I think it would be better if you open your thinking, to include Stepchildren. The amount of single men in the age group that want to marry nearly 40 year old Women, is small, discount Lone Dads and it becomes miniscule.
I've had plenty of friends who have gotten into relationships at 35+, one who couldn't have children is now a doting Step Grandmother, as are others. Or really good Aunts to their new Nieces and Nephews.
It might happen for you, it might not.