Olivia and Astrid had no connection before the series
Olivia and Astrid are first seen "Pilot" episode while entering Walter Bishop's lab. Both were assigned together to work on a case of an Agent's body.
Astrid develops into Walter's full time assistant. Olivia and Astrid become fast friends. Over time, Olivia comes to trust Astrid very deeply. Due to Astrid's constant presence in the lab, Astrid is able to easily access information. This proves to be very important due to Olivia constantly moving around and requiring immediate information, which at the time was inconvient for her to access. This means that Olivia and Astrid develop a bond of trust between each other.
By the begging, they have complete faith in each other
By the time of season five, it is obvious they trust each other readily.