Believers have a New Testament mandate to go and preach the gospel to every person (Mark 16:15). This mandate is repeated in different ways in Matthew, Luke and John, as well as in Acts (Matt 28:18-20; Luke 24:46-47; John 20:21; Acts 1:8). There is no doubt about the believer’s responsibility in spreading the good news of Jesus Christ. The believers in the first church at Jerusalem did exactly that as they were being scattered because of persecution (Acts 8:1, 4).
To get the gospel message to other nations would require a more concerted effort.
The New Testament example of how this is accomplished is found in Acts 13 where a local assembly, under the direction of the Holy Spirit, sent out Barnabas and Saul to preach the gospel to people in other cities and nations. The emphasis is on preaching the gospel, teaching converts and planting churches.