I don't think we were an accident at all, for two reasons.

Firstly, because everything happens for a reason. Causality isn't about 'random chance', it's about action and reaction. Every effect has a cause (and every effect is a cause). Nothing is truly 'random', it just appears that way when you can't percieve the reason behind it.

Secondly, for an event to be an 'accident' it has to be outside of someone's plans or expectations. If the universe has plans, we were obviously in them or we wouldn't be here. If the universe doesn't have plans, it simply can't have accidents either.

As to whether science can explain everything; I'd have to say no. Scientific method is hinged on the ability to separate, name, categorize and define objects. However, not everything can be separated, named, categorized and defined (as difficult as that is for some people to get their heads around).