Scientists have announced that the first Webb data will be released shortly after the first image. More here

Article by: Andacs Robert Eugen, on 13 June 2022, at 11:24 am Los Angeles time
We are all waiting for the first clear color image from the powerful James Webb Telescope which according to NASA is coming on July 12, 2022.
In a statement from the Space Telescope Science Institute, the first data from the telescope will also come shortly after the first image.
They estimate that data will come after about 2 days, around July 14, 2022.
The first data will consist of information on the commissioning of JWST. Later, the telescope will begin to provide scientific data on its observations.
Commissioning data are available for NASA, but will not be released until July 14, when James Webb is expected to have entered Cycle 1 of scientific observations.
We look forward to the first clear color image from the telescope and the first data.