Doctors, nurses, and the elderly rolled up their sleeves across the European Union to receive the first doses of the coronavirus vaccine on Sunday in a symbolic show of unity and a moment of hope for a continent confronting its worst health care crisis in a century.

The coordinated rollout for the 27-nation bloc was aimed at projecting a unified message that the vaccine was safe and Europe’s best chance to emerge from the pandemic and the economic devastation caused by months of lockdown.