Per my answer here;
The Silence needed the suit to physically control River Song. They're aware of the events surrounding his death (e.g. that he's shot by River Song at Lake Silencio on the date in question wearing an Apollo spacesuit) and must have been quite surprised to find that she had no intention of doing so.
Their reaction was to travel further back into time and guide the development of the human race to the point that they'd developed a space suit capable of being used as a physical control device, turning her into a 'people puppet'.
In the episode 'The Impossible Astronaut' River Song says to the Doctor at the moment of his apparent death:
"I can't stop it - the suit's in control".
As to why they didn't try something less convoluted (e.g. altering the entirety of human history just to get hold of a space suit that they could have easily replicated themselves) the answer is that it's not been explained.