If we assume you are conscious while meditating, here are the rules in question with errata:
You can't be surprised while you are conscious. Other creatures don't gain advantage on attack rolls against you as a result of being unseen by you.
During its first turn, the assassin has advantage on attack rolls against any creature that hasn’t taken a turn. Any hit the assassin scores against a surprised creature is a critical hit.
Reading this, the Assassin wants to engage in combat with you. Combat begins; you are not surprised. Everyone rolls initiative.
One might say "but why are you rolling initiative?"; it is simple. You aren't surprised and are in combat. You roll initiative. Normally a pure ambush would be an implied surprise, and they would start combat by making an attack then you roll initiative. But you are immune to surprise, so you get to roll initiative even when you have no warning that you are entering combat.
If you win initiative, you get to act first. You probably do not see the Assassin, so you do not act. The Assassin then attacks you.
The Assassin does not have advantage. The attack is not a critical hit unless it rolls it normally, because you are not surprised.
If you lose initiative, they get to act first. You probably do not see the Assassin. The Assassin attacks you.
The Assassin has advantage, as they are acting prior to you in the combat. The attack is not a critical hit unless it rolls it normally, because you are not surprised.
In no case does the Assassin auto-hit nor does the Assassin auto-crit.
Game fiction wise, you are so alert that even though you had no idea the Assassin was attacking you, as the attack was under way you actually started to dodge it. Your alertness is, basically, superhuman. It is opposed by the superhuman accuracy of the Assassin. Between the two, the Assassin gets a boost, but not nearly as large as against some other random target.