"You shall receive power
when the Holy Spirit has come upon you;
and you shall be witnesses to Me in Jerusalem
and in all Judea and Samaria and to the end of the earth,”
Being witnesses to Christ means to be demonstrators of all that Jesus was and is. In preparation for the arrival of the Holy Spirit Peter reminded everyone present there had to be a replacement to make up the 12.
Of the approximately 120 who were present only a fully qualified man would "become a witness with us of His resurrection” (Acts 1'21-22).
They were obeying what the Lord had told them:
“Behold, I send the Promise of My Father upon you; but tarry in the city of Jerusalem until you are endued with power from on high,” Luke 24'49.
It is important to keep in mind that the Lord said that they would be witnesses and not evangelists. While the idea of "evangelism" is not wrong, it is not what Jesus said Believers' lives would be all about after the Spirit comes.
The proposition that they should evangelise generally makes Believers uncomfortable and they feel somewhat pressured by it.
One of the main points of this study is that Kingdom witnessing is not necessarily equal to doing "the work of an evangelist" (2 Timothy 4'5).
Not surprisingly, those Believers who do "evangelise" comfortably are often God-appointed Evangelists!