Why is specific “that” first day of the week mentioned?
It is important for the writer, and consequently, for the readers of this passage to recognize that earlier that day, Mary of Magdala found the tomb empty, the rock removed from it. After hearing her report of what she found, Peter and the other disciple went to the tomb and found the burial cloths rolled up separately. The other disciple “saw and believed.”
After that, Mary returned to the tomb and met the Risen Jesus. She recognized him when he called her by name. He then told her to “go to my brothers and tell them, ‘I am going to my Father and your Father, to my God and your God.’”
In verse 18, “Mary of Magdala went and announced to the disciples, “I have seen the Lord,” and what he told her.”
And now, in the very next verse, verse 19, we find the fearful disciples who stay behind locked doors “for fear of the Jews”
That was probably the reason for the writer to include the specific time of the encounter of the Risen Christ and the disciples.
To these fearful disciples, Jesus came and gives them peace.
To these unbeliever disciples, who just can't get it, Jesus came and gives them assurance.
Moreover, Jesus commissons these fearful and unbelieving disciples to continue the mission he has received from the Father, As the Father has sent me, so I send you.”
In the end, it’s not about us, whether we are strong or have enough faith or not. It is the Risen Christ who entrusts us, knowing who we are, with the mission the Father has given to him.