The ability to stay alive outside the mother’s womb occurs 22-24 weeks (approximately 5 1/2 months) after conception, but conception is the start of the journey to birth and beyond. So of course life begins at conception. If life did not begin at conception, there would never be growth from zygote to embryo to fetus to infant.
Using the term ‘conception’ in two different contexts causes confusion. The union of the two gametes causes a ‘new life to express’ and the attachment to the uterine lining is a conception, by the mother.