If Leyline of Vitality and a creature enter under your control at the same time, Leyline of Vitality's third ability will trigger.

A player's "opening hand" is the hand of cards the player has after all players have taken mulligans. If players have any cards in hand that allow actions to be taken with them from a player's opening hand, the starting player takes all such actions first in any order, followed by each other player in turn order. Then the first turn begins.