From what I read it's possible for a bird strike to disrupt hydraulics. However there were probably a few additional engineering or pilot errors because that should not prevent a plane from putting down its landing gear, and a lack of landing gear should not prevent the plane from slowing down enough to not crash.

Its cases like these where I think the lining up of Swiss chesse model for failure makes a lot of sense

A bird strike in one engine could disrupt hydraulics yes but not all three circuits. It's weird. I'm sure there's more to this story.

Also the landing gear can be extended though gravity even without hydraulic pressure.