Omar al Bashir was removed by the military after almost 30 years in power.
Release International told Premier the new leadership will have the opportunity to enshrine freedom to worship in the law.
Speaking during Premier's New Hour, Andrew Boyd from the charity explained: "There have been decades now of extreme persecution and Release International's hope is that this could now be a turning point. It is a window of opportunity for things to change.
"And we call on the international community, leaders of the free world, to help Sudan make the transition it needs to become a democracy, and to expect and require and encourage that country to give that most basic freedom that everybody needs.
"And that's the freedom of faith."
Boyd said Christians in the predominantly Muslim country have faced the heaviest oppression in the Nuba Mountains, where the government has been driving out minority groups in a programme of ethnic cleansing.
Churches have also been demolished and church leaders have been arrested, with church property often seized.
The charity said there have been "encouraging signs" for the two million Christians in Sudan since the coup.
The Chief of the Military Council, General Abdel Fattah al-Burhan, has released hundreds of political prisoners and described the recent protests as a "peaceful revolution".
Sudan has been listed by the United States Commission on International Religious Freedom among the world's ten worst violators of religious freedom.
Boyd said while there has been limited media coverage on the persecution of Christians in the African nation, it is important that prayers are said for the people there.
Listen to Premier's Eno Adeogun speaking with Andrew Boyd:
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