After escaping from Shield team, Natasha's family flew from Ohio to Cuba:
This is Shield car chasing Natasha's family in opening scene. Why Natasha's family escaping from Shield team in opening scene?
After escaping from Shield team, Natasha's family flew from Ohio to Cuba:
This is Shield car chasing Natasha's family in opening scene. Why Natasha's family escaping from Shield team in opening scene?
At the start of the film, Natasha and her 'family' (Melina, Alexei and Yelena) are actually deep cover agents acting on behalf of the Soviet government, infiltrating a SHIELD facility performing experiments on the human mind.
Melina: We infiltrated the North Institute in Ohio. It was a front for S.H.I.E.L.D. scientists. In conjunction with the Winter Soldier project, they had dissected and deconstructed the human brain to create the first and only cellular blueprint of the basal ganglia. This was the hub for cognition. Voluntary motor movement, procedural learning.
We didn't steal weaponry or technology. We stole the key to unlocking free will.
Having extracted this vital data on behalf of General Dreykov, they then flee the country, pursued by SHIELD agents.
There's quite a good synopsis here if you want more background.